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

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.

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

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

Define A a unbounded self-adjoint operator on Hilbert space X. Let \( \{ A_n \} \) be its resolvent approximation sequence with closed range \( {\mathcal {R}}(A_n) (n \in \mathrm {N}) \), that is, \( A_n (n \in \mathrm {N}) \) are all self-adjoint on Hilbert space X and $$\begin{aligned} \mathop {s-\lim }\limits _{n \rightarrow \infty } R_\lambda (A_n) = R_\lambda (A)\quad (\lambda \in \mathrm {C}

For \(\gamma >0\) and \(a>0,\) the operator \(P_{a,\gamma }^{t}f\) of Schrödinger type with complex time is defined by $$\begin{aligned} P_{a,\gamma }^{t}f(x)=S_{a}^{t+it^{\gamma }}f(x) =\int _{{\mathbb {R}}} e^{ix\xi }e^{it|\xi |^{a}}e^{-t^{\gamma }|\xi |^{a}} {\hat{f}}(\xi )d\xi , \end{aligned}$$ and the corresponding maximal operator \(P_{a,\gamma }^{*}\) is defined by $$\begin{aligned} P_{a,\gamma

Let X and Y be compact Hausdorff spaces and let \(F:C(X)\rightarrow C(Y)\) be a (non-surjective) coarse \((M,\varepsilon )\)-quasi-isometry with \(M<\sqrt{8/7}\). Assume also that the range of F “approximates” C(Y) well, then X and Y are homeomorphic. Moreover, if \(U:C(X)\rightarrow C(Y)\) is the canonical isometry induced by the homeomorphism, then $$\begin{aligned} \Vert F(f)-MU(f)\Vert \le 8\frac{M^2-1}{M}\Vert

This paper is devoted to study the almost convergent sequence space \(\widehat{c}(\varPhi )\) derived by the Euler totient matrix. It is proved that the space \(\widehat{c}(\varPhi )\) and the space of all almost convergent sequences are linearly isomorphic. Further, the \(\beta \)-dual of the space \(\widehat{c}(\varPhi )\) is determined and Euler totient core of a complex-valued sequence has been

In the classical operator theory, there are several versions of spectra, related to special classes of operators (Fredholm, semi-Fredholm, upper/lower semi-Fredholm, etc.). We generalize these notions for adjointable operators on Hilbert \(C^*\)-modules replacing scalars by the center of the algebra, and show that most relations between these spectra are still true for these generalized versions. The

By introducing the concepts of strongly limited completely continuous and strongly Dunford–Pettis completely continuous subspaces of operator ideals, it will be given some characterizations of these concepts in terms of lcc ness and DPcc ness of all their evaluation operators related to that subspace. In particular, when \(X^*\) or Y has the Gelfand–Phillips (GP) property, we give a characterization

In this article, we give some characterizations of the inner functions in the space of \(W_{\alpha }\). Meanwhile, the zero sets in \(W_{\alpha }\) are also studied.