By means of the weight function, the following results are given. The Hilbert-type multiple integral inequality with the \(\lambda \)-order homogeneous kernel \(\int _{R_{+}^{n}}\int _{R_{+}^{m}}K(\left\| x\right\| _{m,\rho },\left\| y\right\| _{n,\rho })f(x)g(y)\mathrm{d}x\mathrm{d}y\le M\left\| f\right\| _{p,\alpha }\left\| g\right\| _{q,\beta }\) is true if and only if \(\frac{\alpha +m}{p}+\frac{\beta

This paper is concerned with the ergodicity and strong stability for (b, l)-regularized resolvent operator families. First, we study Abel ergodicity and Cesáro ergodicity of (b, l)-regularized resolvent operator families by using the methods of operator theory and complex Tauberian theorem. And then, by constructing a new operator-valued function, we obtain some sufficient conditions on the strong

We revisit an archive submission by Denton et al. (Eigenvectors from eigenvalues: a survey of a basic identity in linear algebra. arXiv:1908.03795v3 [math.RA], 2019) on \(n \times n\) self-adjoint matrices from the point of view of self-adjoint Dirichlet Schrödinger operators on a compact interval.

Our aim in this paper is to consider a generalization of the concept of n-quasi-m-isometric operators of a single operator done in Mahmoud Sid Ahmed et al. (Results Math 73:511–531, 2018) and Mechri and Mahmoud Sid Ahmed (Oper Matrices 14(1): 145–157, 2020) to the multi-dimensional operators. We discuss the most interesting results concerning these classes of tuples of operators by extending some results

For a Young function \(\phi \) and a locally compact second countable group G, let \(L^\phi (G)\) denote the Orlicz space on G. In this paper, we present a necessary and sufficient condition for the topological transitivity of a sequence of cosine operators \(\{C_n\}_{n=1}^{\infty }:=\{\frac{1}{2}(T^n_{g,w}+S^n_{g,w})\}_{n=1}^{\infty }\), defined on \(L^{\phi }(G)\). We investigate the conditions for

By a new method derived from Nicola–Primo–Tabacco in [J Pseudo-Differ Oper Appl 10:359–378 (2019)], we study the boundedness on \(\alpha\)-modulation spaces of unimodular multipliers with symbol \(\mathrm {e}^{\mathrm {i}\mu (\xi )}\). Comparing with the previous results, the boundedness result is established for a larger family of unimodular multipliers under weaker assumptions.

In this paper, we discuss new inequalities for accretive matrices through non-standard domains. In particular, we present several relations for \(A^r\) and \(A\sharp _rB\), when A, B are accretive and \(r\in (-1,0)\cup (1,2).\) This complements the well-established discussion of such quantities for accretive matrices when \(r\in [0,1],\) and provides accretive versions of known results for positive

The original article has been corrected.

In this paper, we consider the non-spectral problem for the planar self-affine measures \(\mu _{M,D}\) generated by an expanding integer matrix \(M\in M_2({\mathbb {Z}})\) and a finite digit set$$\begin{aligned} D=\{(0,0)^t, (\alpha _1,\alpha _2)^t, (\alpha _3, \alpha _4)^t \} \oplus k(\alpha _1\alpha _4-\alpha _2\alpha _3){\mathfrak {D}}, \end{aligned}$$where \(k\in {\mathbb {Z}}\backslash \{0\},

The notion of conjugation is extended to Banach \(*\)-algebras. The aim of this paper is to characterize conjugations on the Banach algebra of all bounded linear operators on a complex Hilbert space, the algebra of J-symmetric operators on a complex Hilbert space with given conjugation J and the algebra of all complex valued continuous functions, defined on a connected locally compact Hausdorff space

Let A and B be \(n\times n\) positive semidefinite matrices, and let \( \alpha ,\beta \in (0,1)\) such that \(\alpha +\beta =1\). Among other inequalities, it is shown that (a) If f is a non-negative concave function on \([0,\infty )\), then$$\begin{aligned} s_{j}(\alpha f(A)+\beta f(B))\le s_{j}(f(\sqrt{2}\left| \alpha A+i\beta B\right| )) \end{aligned}$$for \(j=1,\ldots ,n.\) (b) If f is a non-negative

It is known in the literature that in the RNP Banach space the set valued uniformly integrable martingale is a regular martingale. In this paper by using a selector approach we provide a weaker condition than uniform integrability of a set valued Aumann–Pettis integrable martingale to be a set valued Aumann–Pettis integrable regular martingale. The Converse is also established. As an application of

We present a novel generalization, in Banach spaces, of the celebrated Helly’s principle selection. Specifically, our main result is a quantitative version of such principle selection. Our main tool is the so called Degree of Nondensifiability, which measures (in the specified sense) the distance of a given convex subset of a Banach space to the class of its Peano Continua. As application of our results

Let \(\sigma\) be a non-trivial operator mean in the sense of Kubo and Ando, and let \(OM_+^1\) be the set of normalized positive operator monotone functions on \((0, \infty )\). In this paper, we study the class of \(\sigma\)-subpreserving functions \(f\in OM_+^1\) satisfying$$\begin{aligned} f(A\sigma B) \le f(A)\sigma f(B) \end{aligned}$$for all invertible positive operators A and B. We provide

In this paper, we improve the order of approximation of certain operators linking Bernstein and genuine Bernstein–Durrmeyer operators. Firstly, we obtain some direct results in terms of modulus of continuity and Voronovskaja type asymptotic formula for these operators. Finally, we give some numerical examples regarding the obtained theoretical results for new constructed operators.

Let E be a \(W^{*}\)-correspondence and let \(H^{\infty }(E)\) be the associated Hardy algebra. The unit disc of intertwiners \(\mathbb {D}((E^{\sigma })^{*})\) plays a central role in the study of \(H^{\infty }(E)\). We show a number of results related to groups of automorphisms of both \(H^{\infty }(E)\) and \(\mathbb {D}((E^{\sigma })^{*})\). We find a matrix representation for these groups and

This paper is devoted to study a class of p-Kirchhoff equation with critical exponent. The existence and multiplicity of positive solutions to this equation are obtained by the variational methods.

Complex symmetry operators have notable applications in extension and dilation results, rank one perturbations of Jordan operators, matrix-valued inner functions and free interpolation theory in the disk and so on. While in the study of the complex symmetric operators, one of the problems one always encounters is when a C\(^*\)-algebra singly generated contains no nonzero compact operators. In this

In this paper, the authors define the weak Herz spaces and the weak Herz-type Hardy spaces with variable exponent. As applications, the authors establish the boundedness for a class of singular integral operators including some critical cases.

A function from a closed interval [a, b] to a Banach space X is regulated if all one-sided limits exist at each point of the interval. A function \(\alpha\) from [a, b] to the space of all bounded linear transformations from X to a Banach space Y is an integrator for the regulated functions if, for each regulated function f, the Riemann-Stieltjes sums of f, with sampling points from the interiors of

Let \({\mathcal {B}}_{Id}({\mathcal {H}})\) be the set of all idempotents on a Hilbert space \({\mathcal {H}}.\) We give characterizations of the star partial order on \({\mathcal {B}}_{Id}({\mathcal {H}})\) with respect to a particular space decomposition, which is related to Halmos’ two projections theory. Using this, we investigate the lattice properties of \({\mathcal {B}}_{Id}({\mathcal {H}})\)

In this paper, we give an elementary approach to the numerical radius and norms of the real and imaginary parts of a quadratic operator in terms of its norm. This method is based on proving equality of the numerical radius with one of its suitable upper bounds, via successively establishing equality of the numerical radius with some of its intermediate upper bounds. Meanwhile, some other related results

In this paper, we present some Heinz mean inequalities for sector matrices involving positive linear maps which generalize the results of Mao et al. Moreover, we give some inequalities involving the mean of inverse sector matrices and the inverse of the mean of sector matrices involving positive linear maps.

In this paper we characterize the Birkhoff–James orthogonality with respect to the numerical radius norm \(v(\cdot )\) in \(C^*\)-algebras. More precisely, for two elements a, b in a \(C^*\)-algebra \(\mathfrak {A}\), we show that \(a\perp _{B}^{v} b\) if and only if for each \(\theta \in [0, 2\pi )\), there exists a state \(\varphi _{_{\theta }}\) on \(\mathfrak {A}\) such that \(|\varphi _{_{\theta

In this paper, we prove a density and a duality results in Musielak spaces, as well as an inequality of type Poincaré, assuming only the log-Hölder continuity condition. We will apply these results to give in non reflexive Musielak spaces the existence of solutions for some nonlinear parabolic problems with no continuous lower order terms.

In this paper we present \(L^2\) and \(L^p\) versions of the geometric Hardy inequalities in half-spaces and convex domains on stratified (Lie) groups. As a consequence, we obtain the geometric uncertainty principles. We give examples of the obtained results for the Heisenberg and the Engel groups.

In this paper, we introduce a closed subspace \({\mathcal {H}}^{p(\cdot ),\infty }({{\mathbb {R}}}^n)\) of variable weak Hardy spaces \(H^{p(\cdot ),\infty }({{\mathbb {R}}}^n)\), and give the dual space of \({\mathcal {H}}^{p(\cdot ),\infty }({{\mathbb {R}}}^n)\) with the variable exponent function \(p(\cdot ): \mathbb {R}^n \rightarrow (0,\infty )\) satisfying the globally log-Hölder continuous condition

For the Dunkl transforms associated with the weight functions \(h_{\kappa }^2(x)=\prod _{j=1}^d |x_j|^{2{\kappa }_j}\), \({\kappa }_1,\ldots , {\kappa }_d\ge 0\) on \({{\mathbb {R}}}^d\), it is proved that if \(p\ge 2\) and \({\delta }>{\delta }_{\kappa }(p):=\max \{(2l_{\kappa }+1) |\frac{1}{2}-\frac{1}{p}|-\frac{1}{2},0\}\), the Bochner–Riesz means \(B_{R}^{\delta }(h_{\kappa }^2; f)\) converges

The goal of this paper is to characterize the local sharp estimate \((I_{\rho } f)^{\#}(x) \le C \, M_{\rho } f(x)\) and by using this inequality to get necessary and sufficient conditions on the triple functions \((\varphi , \rho , \omega )\) which satisfy the equivalence of norms of the generalized fractional integral operator \(I_{\rho }\) and the generalized fractional maximal operator \(M_{\rho

This note is devoted to a weaker version of Bishop property \(\beta\) at a given complex number. We show in particular that this notion is a regularity and hence the induced spectrum satisfies all classical properties of the spectrum.

We introduce a concept of complete proximal normal structure and used to investigate the existence of a best proximity point for an arbitrary family of cyclic relatively nonexpansive mappings in the setting of strictly convex Banach spaces. We also prove that every bounded, closed and convex pair in uniformly convex Banach spaces as well as every compact and convex pairs in Banach spaces has complete

On the unit ball in the n dimensional complex Euclidean space, we introduce a new weighted Bergman space and Toeplitz operators. By Berezin transform and average functions, we estimate the essential norms of the Toeplitz operators.

For each analytic map \(\psi\) on the complex plane \(\mathbb {C}\), we study the Ritt’s resolvent growth condition for the composition operator \(C_{\psi} :f \rightarrow f\circ \psi\) on the Fock space \({\mathcal {F}}_2\). We show that \(C_{\psi}\) satisfies such a condition if and only if it is either compact or reduces to the identity operator. As a consequence, it is shown that the Ritt’s resolvent

In this article, we investigate some classes of dominated orthogonally additive operators in lattice-normed spaces. We say that an orthogonally additive operator T from a lattice-normed space (V, E) to a lattice-normed space (W, F) is completely additive if, for every order summable family of pairwise disjoint elements \((v_{\alpha })_{\alpha \in \Lambda }\) of V, the family \((Tv_{\alpha })_{\alpha

In this paper, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space \(\mathcal {H}\), which are bounded with respect to the seminorm induced by a positive operator A on \(\mathcal {H}\). Mainly, we show that \(r_A(T)\le \omega _A(T)\) for every A-bounded operator T, where \(r_A(T)\) and \(\omega _A(T)\) denote respectively the A-spectral

In this work, we describe well-defined dissipative boundary conditions related with a singular third-order differential equation in lim-3 case at singular point. Using the characteristic function of the corresponding dissipative operator we introduce a completeness theorem.

In this paper, on \({\mathbb {D}}\) we define Cowen–Douglas function introduced by the Cowen–Douglas operator \(M_\phi ^*\) on Hardy space \({\mathcal {H}}^2({\mathbb {D}})\), moreover, we give a necessary and sufficient condition to determine when \(\phi\) is a Cowen–Douglas function, where \(\phi \in {\mathcal {H}}^\infty ({\mathbb {D}})\) and \(M_{\phi }\) is the associated multiplication operator

Let \({\mathcal {H}}\), \({\mathcal {K}}\) be Hilbert spaces over \({\mathbb {F}}\) with \(\dim {\mathcal {H}}\ge 3\), where \({\mathbb {F}}\) is the real or complex field. Assume that \(\varphi :{B}({\mathcal {H}})\rightarrow {B}({\mathcal {K}})\) is an additive surjective map and \(r\ge 3\) is a positive integer. It is shown that \(\varphi \) is r-nilpotent perturbation of scalars preserving in both

This paper is concerned with general \(n\times n\) upper-triangular operator matrices with given diagonal entries. The characterizations of perturbations of their left (right) essential spectrum and essential spectrum are given, based on the space decomposition technique. Moreover, some sufficient and necessary conditions are given under which the left (right) essential spectrum and the essential spectrum

We study inductive limit in the category of ternary ring of operator (TRO). The existence of inductive limit in this category is proved and its behaviour with quotienting is discussed. For a TRO V, if A(V) is the linking \(C^{*}\)-algebra generated by V, then we investigate whether it commutes with inductive limits of TROs, in the sense that if \((V_n,f_n)\) is an Inductive system then \(\varinjlim

The present paper deals with the A-statistical approximation processes of the general class of integral type linear positive operators including many well-known operators in the \(L_{p}\)-metric spaces.

We derive some inequalities involving first four central moments of discrete and continuous distributions. Bounds for the eigenvalues and spread of a matrix are obtained when all its eigenvalues are real. Likewise, we discuss bounds for the roots and span of a polynomial equation.

Let \(B_s(H)\) denote the set of all bounded selfadjoint operators acting on a separable complex Hilbert space H of dimension \(\ge 2\). Also, let \({\mathcal {S}}{\mathcal {A}}_s(H)\) (esp. \({\mathcal {I}}{\mathcal {A}}_s(H)\)) denote the class of all singular (resp. invertible) algebraic operators in \(B_s(H)\). Assume \({\varPhi }:B_s(H)\rightarrow B_s(H)\) is a unital additive surjective map such

Let A be an infinite dimensional simple unital stably finite C*-algebra and B be a large subalgebra of A. In this paper, we show that B has local weak comparison if A has local weak comparison, and A has local weak comparison if \(M_{2}(B)\) has local weak comparison. As a consequence, we are able to prove that A has weak comparison if and only if B has weak comparison.

In the present paper, we discuss the approximation properties of certain link integral modification of Ismail–May operators. We point out here that the operators of Ismail–May can also be derived from the Jain operators. We also establish some direct convergence estimates including error, difference estimates and an asymptotic formula in simultaneous approximation. In the end, we indicate through graphical

We present a complete characterization of the metric compactification of \(L_{p}\) spaces for \(1\le p < \infty \). Each element of the metric compactification of \(L_{p}\) is represented by a random measure on a certain Polish space. By way of illustration, we revisit the \(L_{p}\)-mean ergodic theorem for \(1< p < \infty \), and Alspach’s example of an isometry on a weakly compact convex subset of

We study geometric properties of GL-spaces. We demonstrate that every finite-dimensional GL-space is polyhedral; that in dimension 2 there are only two, up to isometry, GL-spaces, namely the space whose unit sphere is a square (like \(\ell _\infty ^2\) or \(\ell _1^2\)) and the space whose unit sphere is an equilateral hexagon. Finally, we characterise the spaces \(E = ({{\mathbb {R}}}^n, \Vert \cdot

Let \(\mathcal {W}\) be an ideal of compact operators A in a Banach space X satisfying the condition \(N_\mathcal {W}(A)=\sum _{k=1}^{\infty }x_k(A)<\infty \), where \(x_k(A)\)\((k=1, 2, \ldots )\) are the Weyl numbers of A. It is proved that for all \(A\in \mathcal {W}\) and any regular \(\lambda \ne 0\) of A, the inequality$$\begin{aligned} \Vert \det \;(I-\lambda ^{-1}A)(\lambda I-A)^{-1}\Vert \le

In this paper, we investigate commuting dual truncated Toeplitz operators on the orthogonal complement of the model space \(K^{2}_{u}.\) Let \(f,g \in L^{\infty },\) if two dual truncated Toeplitz operators \(D_{f}\) and \(D_{g}\) commute, we obtain similar conditions of Brown–Halmos Theorem for Hardy-Toeplitz operators, that is, both f and g are analytic, or both f and g are co-analytic, or a nontrivial

We study the bounded endomorphisms of \(\ell ^2(G)\times \dots \times \ell ^2(G)=\ell _{N}^2(G)\) that commute with translations, where G is a discrete abelian group. It is shown that they form a C*-algebra isomorphic to the C*-algebra of \(N\times N\) matrices with entries in \(L^\infty ({\widehat{G}})\), where \({\widehat{G}}\) is the dual space of G. Characterizations of when these endomorphisms

Let A and B be strictly positive linear operators on Hilbert space \({\mathcal {H}}\) and \(n\in {\mathbb {N}}\). We define the n-th relative operator entropy$$\begin{aligned}&S^{[n]}(A|B) \equiv \frac{1}{n!}A^{\frac{1}{2}} (\log A^{-\frac{1}{2}}BA^{-\frac{1}{2}})^n A^{\frac{1}{2}} = \displaystyle \frac{1}{n!} A(A^{-1}S(A|B))^n \end{aligned}$$and the n-th Tsallis relative operator entropy \(T^{[n]}_x(A|B)\)

Let \(L=-\varDelta +V\) be a Schrödinger operator acting on \(L^2({\mathbb {R}}^{d})\), where V belongs to the reverse Hölder class \(B_q\) for some \(q\ge d\). For \(\alpha , \beta \in [0,1)\), let \(\varLambda _{\alpha ,\beta }^L({\mathbb {R}}^d)\) be the Campanato–Sobolev space associated with L. Via the Poisson semigroup \(\{e^{-t\sqrt{L}}\}_{t\ge 0}\), we extend \(\varLambda _{\alpha ,\beta }^L({\mathbb

Let \((M^{n},g,e^{-f}dv)\) be a complete smooth metric measure space. We prove elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation$$\begin{aligned} \left( \varDelta _{f}-\frac{\partial }{\partial t}\right) u(x,t)+q(x,t)u(x,t)+au(x,t)(\ln u(x,t))^{\alpha }=0, \end{aligned}$$where \((x,t)\in M\times (-\infty ,\infty )\) and a, \(\alpha \) are arbitrary constants

In this paper, we investigate the existence of the extremal solutions for a class of impulsive fractional integro-differential equation with order \(1< \alpha < 2\), combine upper and lower solution method with the theory of \((\alpha ,\beta )\)-resolvent family, a series of results about the solutions to such differential equations is obtained. The results improve and extend some relevant results

A pair of Banach spaces (X, Y) is said to be coarsely stable if for every coarse Lipschitz embedding \(f: X\rightarrow Y\), there exist \(\alpha ,\gamma >0\) and a Lipschitz mapping \(T:L(f)\rightarrow X\) with its Lipschitz constant \(\Vert T\Vert _{Lip}\le \alpha \) such that \(\Vert Tf(x)-x\Vert \le \gamma \) for all \(x\in X\), where L(f) is the closed linear span of f(X). In this paper, we study

The boundedness and the compactness of weighted composition operators from the minimal Möbius invariant space into n-th weighted-type spaces are studied in this paper. Moreover, some estimates for the essential norm of weighted composition operators are also investigated.

Let \( \mathcal {A} \) and \(\mathcal {B}\) be two unital \(C^*\)-algebras such that \( \mathcal {A} \) contains a non-trivial projection \(P_1\). In this paper, we investigate the additivity of maps \( \varPhi \) from \(\mathcal {A}\) onto \(\mathcal {B}\) that are bijective maps, that satisfy$$\begin{aligned} \varPhi \left( \frac{AB^*C+CB^*A}{2} \right) =\frac{\varPhi (A)\varPhi (B)^*\varPhi (C)+\varPhi

Let (X, d) be a metric space and let \(\mathrm{Lip}(X,d) \) denote the complex algebra of all complex-valued bounded functions f on X for which f is a Lipschitz function on \(\mathrm{(X,d)}\). In this paper we give a complete description of all 2-local real and complex uniform isometries between \(\mathrm{Lip}(X,d) \) and \(\mathrm{Lip(Y},\rho \mathrm{)}\), where (X, d) and \((Y,\rho )\) are compact

In this paper we prove a Sobolev–Spanne type \({\,^{^{\complement }}\!\mathcal M}_{\{x_0\}}^{p(\cdot ),\omega } (\varOmega )\rightarrow {\,^{^{\complement }}\!\mathcal M}_{\{x_0\}}^{q(\cdot ),\omega } (\varOmega )\)-theorem for the potential operators \(I^{\alpha }\), where \({\,^{^{\complement }}\!\mathcal M}_{\{x_0\}}^{p(\cdot ),\omega }(\varOmega )\) is local “complementary” generalized Morrey spaces

The purpose of this article is to present the second type fundamental relationship between the generalized Fourier–Feynman transform and the generalized convolution product on Wiener space. The relationships in this article are also natural extensions (to the case on an infinite dimensional Banach space) of the structure which exists between the Fourier transform and the convolution of functions on