• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-20
Richard Lechner, Pavlos Motakis, Paul F. X. Müller, Thomas Schlumprecht

We introduce the concept of strategically reproducible bases in Banach spaces and show that operators which have large diagonal with respect to strategically reproducible bases are factors of the identity. We give several examples of classical Banach spaces in which the Haar system is strategically reproducible: multi-parameter Lebesgue spaces, mixed-norm Hardy spaces and most significantly the space

更新日期：2020-05-20
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-20
Leo Margolis, Ofir Schnabel

Similarly to how the classical group ring isomorphism problem asks, for a commutative ring R, which information about a finite group G is encoded in the group ring RG, the twisted group ring isomorphism problem asks which information about G is encoded in all the twisted group rings of G over R. We investigate this problem over fields. We start with abelian groups and show how the results depend on

更新日期：2020-05-20
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-20
Soumitra Ghara

Let Möb denote the group of biholomorphic automorphisms of the unit disc and (Möb · T) be the orbit of a Hilbert space operator T under the action of Möb. If the quotient , where is the similarity between two operators is a singleton, then the operator T is said to be weakly homogeneous. In this paper, we obtain a criterion to determine if the operator Mz of multiplication by the coordinate function

更新日期：2020-05-20
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-20
Eliana Barriga

We study definably compact definably connected groups definable in a sufficiently saturated real closed field R. Our main result is that for such a kind of groups G that are also abelian, there is a Zariski-connected R-algebraic group H such that the o-minimal universal covering group of G is, up to a locally definable isomorphism, an open connected locally definable subgroup $$\mathcal{W}$$ of the

更新日期：2020-05-20
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-20
Hidefumi Ohsugi, Akiyoshi Tsuchiya

Stanley introduced a lattice polytope $$\mathscr{C}_P$$ arising from a finite poset P, which is called the chain polytope of P. The geometric structure of $$\mathscr{C}_P$$ has good relations with the combinatorial structure of P. In particular, the Ehrhart polynomial of $$\mathscr{C}_P$$ is given by the order polynomial of P. In the present paper, associated to P, we introduce a lattice polytope ℰP

更新日期：2020-05-20
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-20
Michael Lieberman, Jiří Rosický, Sebastien Vasey

Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from [LRV19b], we examine set-theoretic problems related to internal sizes and prove several Löwenheim–Skolem theorems for accessible categories. For example, assuming the singular cardinal hypothesis, we show that a large accessible category has an object in all

更新日期：2020-05-20
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-20
Hezi Halawi, Avner Segal

In this paper, we study the reducibility of degenerate principal series of the simple, simply-connected exceptional group of type E6. Furthermore, we calculate the maximal semi-simple subrepresentation and quotient of these representations.

更新日期：2020-05-20
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-20
Konrad Engel, Themis Mitsis, Christos Pelekis, Christian Reiher

Let n be an integer with n ≥ 2. A set A ⊆ ℝn is called an antichain (resp. weak antichain) if it does not contain two distinct elements x = (x1, …, xn) and y = (y1, …, yn) satisfying xi ≤ yi (resp. xi < yi) for all i ∈ {1, …, n}. We show that the Hausdorff dimension of a weak antichain A in the n-dimensional unit cube [0, 1]n is at most n − 1 and that the (n − 1)-dimensional Hausdorff measure of A

更新日期：2020-05-20
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-20
Andreas Maurischat

This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative differential field which is finitely generated over its algebraically closed field of constants. We also introduce the notion of equivalence of iterative derivations on a

更新日期：2020-05-20
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-20
Moti Gitik

We deal with some questions related to κ-compact cardinals.

更新日期：2020-05-20
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-14
Mahir Bilen Can, Yonah Cherniavsky

We define combinatorially a partial order on the set partitions and show that it is equivalent to the Bruhat-Chevalley-Renner order on the upper triangular matrices. By considering subposets consisting of set partitions with a fixed number of blocks, we introduce and investigate “Stirling posets.” As we show, the Stirling posets have a hierarchy and they glue together to give the whole set partition

更新日期：2020-05-14
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-14
Anton A. Klyachko, Maria A. Ryabtseva

The Gordon-Rodriguez-Villegas theorem says that, in a finite group, the number of solutions to a system of coefficient-free equations is divisible by the order of the group if the rank of the matrix composed of the exponent sums of the j-th unknown in the i-th equation is less than the number of unknowns. We obtain analogues of this and similar facts for algebraic groups. In particular, our results

更新日期：2020-05-14
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-14
Ilijas Farah, Ilan Hirshberg, Alessandro Vignati

We discuss the existence of (injectively) universal C*-algebras and prove that all C*-algebras of density character ℵ1 embed into the Calkin algebra, Q(H). Together with other results, this shows that each of the following assertions is relatively consistent with ZFC: (i) Q(H) is a 2ℵ0-universal C*-algebra. (ii) There exists a 2ℵ0-universal C*-algebra, but Q(H) is not 2ℵ0-universal, (iii) A 2ℵ0-universal

更新日期：2020-05-14
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-14
Cheryl E. Praeger, Jacqui Ramagge, George A. Willis

It is shown that a flat subgroup, H, of the totally disconnected, locally compact group G decomposes into a finite number of subsemigroups on which the scale function is multiplicative. The image, P, of a multiplicative semigroup in the quotient, H/H(1), of H by its uniscalar subgroup has a unique minimal generating set which determines a natural Cayley graph structure on P. For each compact, open

更新日期：2020-05-14
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-14
Hailong Dao, Ilya Smirnov

Let (R, m) be a local ring of characteristic p > 0 and M a finitely generated R-module. In this note we consider the limit $$\mathop {\lim }\limits_{n \to \infty } \frac{{l(H_m^0({F^n}(M)))}}{{{p^{n\dim R}}}}$$ where F(-) is the Peskine-Szpiro functor. A consequence of our main results shows that the limit always exists when R is excellent, equidimensional and has an isolated singularity. Furthermore

更新日期：2020-05-14
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-14
Will Grodzicki

We realize the non-split Bessel model of Novodvorsky and Piatetski-Shapiro in [22] as a generalized Gelfand-Graev representation of GSp(4), as suggested by Kawanaka in [17]. With uniqueness of the model already established in [22], we establish existence of a Bessel model for unramified principal series representations. We then connect the Iwahori-fixed vectors in the Bessel model to a linear character

更新日期：2020-05-14
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-14
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo

We study properties of generic elements of groups of isometries of hyperbolic spaces. Under general combinatorial conditions, we prove that loxodromic elements are generic (i.e., they have full density with respect to counting in balls for the word metric in the Cayley graph) and translation length grows linearly. We provide applications to a large class of relatively hyperbolic groups and graph products

更新日期：2020-05-14
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-14
Sebastián Reyes-Carocca

In this article we study compact Riemann surfaces with a non-large group of automorphisms of maximal order, namely, compact Riemann surfaces of genus g with a group of automorphisms of order 4g–4. Under the assumption that g–1 is prime, we provide a complete classification of them and determine isogeny decompositions of the corresponding Jacobian varieties.

更新日期：2020-05-14
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-14
Udayan B. Darji, Kende Kalina, Márton Elekes, Viktor Kiss, Zoltán Vidnyánszky

In order to understand the structure of the “typical” element of a homeomorphism group, one has to study how large the conjugacy classes of the group are. When typical means generic in the sense of Baire category, this is well understood; see, e.g., the works of Glasner and Weiss, and Kechris and Rosendal. Following Dougherty and Mycielski we investigate the measure theoretic dual of this problem,

更新日期：2020-05-14
• Isr. J. Math. (IF 0.764) Pub Date : 2020-05-14
Samuel M. Corson

We prove that groups for which every countable subgroup is free (ℵ1-free groups) are n-slender, cm-slender, and lcH-slender. In particular, every homomorphism from a completely metrizable group to an ℵ1-free group has an open kernel. We also show that ℵ1-free abelian groups are lcHslender, which is especially interesting in light of the fact that some ℵ1-free abelian groups are neither n-slender nor

更新日期：2020-05-14
• Isr. J. Math. (IF 0.764) Pub Date : 2020-04-04
Daniele Puglisi

Let Ω ⊆ ℝn be a non-empty open bounded set and h: Ω → ℝ be a non-negative continuous function. We prove that for any u ∈ C2(Ω) ∩ C1($$\overline{\Omega}$$) solution of the Monge–Ampère equation $${\rm{det}}(D^2u)=h\;\;{\rm{in}}\;\Omega,$$ , then ∇u satisfies the convex hull property: ∇u(Ω) ⊆ conv(∇u(∂Ω)).

更新日期：2020-04-04
• Isr. J. Math. (IF 0.764) Pub Date : 2020-04-04
Iwona Chlebicka

Under various conditions on the data we analyze how the appearance of lower order terms affects the gradient estimates on solutions to a general nonlinear elliptic equation of the form $$- {\rm{div}}\;a\left( {x,Du} \right) + b\left( {x,u} \right) = \mu$$ with data μ not belonging to the dual of the natural energy space but to Lorentz/Morrey-type spaces. The growth of the leading part of the operator

更新日期：2020-04-04
• Isr. J. Math. (IF 0.764) Pub Date : 2020-04-04
Philipp Lücke

We study partition properties for uncountable regular cardinals that arise by restricting partition properties defining large cardinal notions to classes of simply definable colourings. We show that both large cardinal assumptions and forcing axioms imply that there is a homogeneous closed unbounded subset of ω1 for every colouring of the finite sets of countable ordinals that is definable by a Σ1-formula

更新日期：2020-04-04
• Isr. J. Math. (IF 0.764) Pub Date : 2020-04-04
Costantino Delizia, Urban Jezernik, Primož Moravec, Chiara Nicotera

We show that there is a positive constant δ < 1 such that the probability of satisfying either the 2-Engel identity [X1, X2, X2] = 1 or the metabelian identity [[X1, X2], [X3, X4]] = 1 in a finite group is either 1 or at most δ

更新日期：2020-04-04
• Isr. J. Math. (IF 0.764) Pub Date : 2020-04-04
Christopher Goodrich, Carlos Lizama

We utilize a new definition for the fractional delta operator and prove that it is equivalent by translation to the more commonly used operator. By means of the convolution operation we demonstrate that this new operator is strongly connected to the positivity, monotonicity, and convexity of the functions on which it operates. We also analyze the case of compositions of discrete fractional operators

更新日期：2020-04-04
• Isr. J. Math. (IF 0.764) Pub Date : 2020-04-04
Igor E. Chyzhykov

We propose a new approach for studying asymptotic behaviour of pth means of the logarithmic potential and classes of analytic and subharmonic functions in the unit disc. In particular, we generalize a criterion due to G. MacLane and L. Rubel of boundedness of the L2-norm of log |B|, where B is a Blaschke product, in several directions. We describe growth and decrease of pth means, p ∈ (1,∞), for nonpositive

更新日期：2020-04-04
• Isr. J. Math. (IF 0.764) Pub Date : 2020-04-04
Sherwood Hachtman, Dima Sinapova

For an inaccessible cardinal κ, the super tree property (ITP) at κ holds if and only if κ is supercomact. However, just like the tree property, it can hold at successor cardinals. We show that ITP holds at the successor of the limit of ω many supercompact cardinals. Then we show that it can consistently hold at ℵω+1. We also consider a stronger principle, ISP and certain weaker variations of it. We

更新日期：2020-04-04
• Isr. J. Math. (IF 0.764) Pub Date : 2020-04-04
Artem Dudko, Rostislav Grigorchuk

We study the question of whether or not it is possible to determine a finitely generated group G up to some notion of equivalence from the spectrum sp(G) of G. We show that the answer is “No” in a strong sense. As a first example we present the collection of amenable 4-generated groups Gω, ω ∈ {0, 1, 2}ℕ, constructed by the second author in 1984. We show that among them there is a continuum of pairwise

更新日期：2020-04-04
• Isr. J. Math. (IF 0.764) Pub Date : 2020-04-04
Pablo Cubides Kovacsics, Françoise Delon

In this article we study definable functions in tame expansions of algebraically closed valued fields. For a given definable function we have two types of results: type (I), which hold in a neighborhood of infinity, and type (II), which hold locally for all but finitely many points in the domain of the function. In the first part of the article, we show type (I) and (II) results concerning factorizations

更新日期：2020-04-04
• Isr. J. Math. (IF 0.764) Pub Date : 2020-04-04
Yair Hayut, Asaf Karagila

We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the Axiom of Choice this is equivalent to measurability, but it is wellknown that Choice is necessary for the equivalence. Oddly enough, this central notion was never investigated on its own before. We prove a technical criterion for lifting elementary embeddings

更新日期：2020-04-04
• Isr. J. Math. (IF 0.764) Pub Date : 2020-03-16
Marcelo Campos

We study the number of s-element subsets J of a given abelian group G, such that ∣J + J∣ ≤ K∣J∣. Proving a conjecture of Alon, Balogh, Morris and Samotij, and improving a result of Green and Morris, who proved the conjecture for K fixed, we provide an upper bound on the number of such sets which is tight up to a factor of 2o(s), when G = ℤ and K = ο(s/(log n)3). We also provide a generalization of

更新日期：2020-03-16
• Isr. J. Math. (IF 0.764) Pub Date : 2020-03-16
Jeff Kahn, Jinyoung Park

Let Qd be the d-dimensional hypercube and N = 2d. We prove that the number of (proper) 4-colorings of Qd is asymptotically 6e2N, as was conjectured by Engbers and Galvin in 2012. The proof uses a combination of information theory (entropy) and isoperimetric ideas originating in work of Sapozhenko in the 1980’s.

更新日期：2020-03-16
• Isr. J. Math. (IF 0.764) Pub Date : 2020-03-16
Shoham Letzter, Julian Sahasrabudhe

For a positive integer k, we say that a graph is k-existentially complete if for every 0 ⩽ a ⩽ k, and every tuple of distinct vertices x1, …, xa, y1, …, yk−a, there exists a vertex z that is joined to all of the vertices x1, …, xa and to none of the vertices y1, …, yk−a. While it is easy to show that the binomial random graph Gn,1/2 satisfies this property (with high probability) for k = (1 − o(1))

更新日期：2020-03-16
• Isr. J. Math. (IF 0.764) Pub Date : 2020-03-16
Gustavo Araújo, Per H. Enflo, Gustavo A. Muñoz-Fernández, Daniel L. Rodríguez-Vidanes, Juan B. Seoane-Sepúlveda

When for the first time, in 1987, a Banach space X and a bounded operator T: X → X without nontrivial invariant subspaces was constructed, one of the many tools used was a series of estimates on the norm of a product of polynomials. Here, we continue this study of estimates on the norm of a product of polynomials by, on the one hand, extending some results due to Beauzamy and Enflo and, on the other

更新日期：2020-03-16
• Isr. J. Math. (IF 0.764) Pub Date : 2020-03-16

Exploiting several ℓp-factorization results for strictly singular operators, we study the strict singularity of the multiplication operator LARB: T → ATB on ℒ(X) for various Banach spaces X.

更新日期：2020-03-16
• Isr. J. Math. (IF 0.764) Pub Date : 2020-03-16
Zilin Jiang, Alexandr Polyanskii

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Let $${\mathcal F}\left( \lambda \right)$$ be the family of connected graphs of spectral radius ≤ λ. We show that $${\mathcal F}\left( \lambda \right)$$ can be defined by a finite set of forbidden subgraphs if and only if $$\lambda > \lambda *: = \sqrt {2 + \sqrt 5 } \approx 2.058$$ and λ ∉ {α2, α3, …}, where $${\alpha 更新日期：2020-03-16 • Isr. J. Math. (IF 0.764) Pub Date : 2020-03-16 Jan Dobrowolski, Frank O. Wagner An ω-categorical group of finite burden is virtually finite-by-abelian; an ω-categorical ring of finite burden is virtually finite-by-null; an ω-categorical NTP2 ring is nilpotent-by-finite. 更新日期：2020-03-16 • Isr. J. Math. (IF 0.764) Pub Date : 2020-03-16 Vladimir I. Chernosov, Andrei S. Rapinchuk, Igor A. Rapinchuk We prove that the genus of a finite-dimensional division algebra is finite whenever the center is a finitely generated field of any characteristic. We also discuss potential applications of our method to other problems, including the finiteness of the genus of simple algebraic groups of type G2. These applications involve the double cosets of adele groups of algebraic groups over arbitrary finitely 更新日期：2020-03-16 • Isr. J. Math. (IF 0.764) Pub Date : 2020-03-16 Tushar Kanta Naik, Rahul Dattatraya Kitture, Manoj K. Yadav It is proved, for a prime p > 2 and an integer n ≥ 1, that finite p-groups of nilpotency class 3 and having only two conjugacy class sizes, 1 and pn, exist if and only if n is even; moreover, for a given even positive integer n, such a group is unique up to isoclinism (in the sense of Philip Hall). 更新日期：2020-03-16 • Isr. J. Math. (IF 0.764) Pub Date : 2020-03-13 Noé Bárcenas, José Cantarero We show that the twisted K-theory of the classifying space of a p-local finite group is isomorphic to the completion of the Grothendieck group of twisted representations of the fusion system with respect to the augmentation ideal of the representation ring of the fusion system. We use this result to compute the K-theory of the Ruiz-Viruel exotic 7-local finite groups. 更新日期：2020-03-13 • Isr. J. Math. (IF 0.764) Pub Date : 2020-02-12 Michel Belliart Let G be a simply connected nilpotent Lie group, let M be a compact connected manifold with dim(M) = dim(G)+1 and let Φ be a C∞ locally free action of G on M. If G admits no lattice and if the centralizer in G of its derived group G′ is the center of G′, then Φ is differentiably orbitally conjugated to a homogeneous action of the same kind. 更新日期：2020-02-12 • Isr. J. Math. (IF 0.764) Pub Date : 2020-02-12 Uri Grupel In this paper we compare the different phenomena that occur when intersecting geometric objects with random geodesics on the unit sphere and inside convex bodies. On the high dimensional sphere we see that with probability bounded away from zero, the observed length will deviate from the actual measure by at most a fixed error for any subset, while in convex bodies we can always choose a subset for 更新日期：2020-02-12 • Isr. J. Math. (IF 0.764) Pub Date : 2020-02-12 Fedor Petrov, Cosmin Pohoata Let G be a finite group, and let r3(G) represent the size of the largest subset of G without non-trivial three-term progressions. In a recent breakthrough, Croot, Lev and Pach proved that r3(\(C_4^{n}$$) ≤ (3.611)n, where Cm denotes the cyclic group of order m. For finite abelian groups $$G \cong \prod\nolimits_{i = 1}^n {{C_{{m_i}}}}$$, where m1,…,mn denote positive integers such that m1 |…|mn, this

更新日期：2020-02-12
• Isr. J. Math. (IF 0.764) Pub Date : 2020-02-12
Gianluca Paolini, Saharon Shelah

In [6], given a metrizable profinite group G, a cardinal invariant of the continuum $$\mathfrak{fm}$$(G) was introduced, and a positive solution to the Haar Measure Problem for G was given under the assumption that non($$\mathcal{N}$$) ≤ $$\mathfrak{fm}$$(G). We prove here that it is consistent with ZFC that there is a metrizable profinite group G* such that non($$\mathcal{N}$$) > $$\mathfrak{fm}$$(G*)

更新日期：2020-02-12
• Isr. J. Math. (IF 0.764) Pub Date : 2020-01-17
Mark F. Hagen, Tim Susse

Let χ be a proper CAT(0) cube complex admitting a proper cocompact action by a group G. We give three conditions on the action, any one of which ensures that χ has a factor system in the sense of [BHS17]. We also prove that one of these conditions is necessary. This combines with [BHS17] to show that G is a hierarchically hyperbolic group; this partially answers questions raised in [BHS17, BHS19].

更新日期：2020-01-17
• Isr. J. Math. (IF 0.764) Pub Date : 2020-01-17
Haruyoshi Tanaka

We consider a perturbed system ($$\Sigma_A^+$$,ϕ(ϵ, ·)) with topologically transitive subshift of finite type $$\Sigma_A^+$$ and Hölder continuous functions ϕ(ϵ, ·) defined on $$\Sigma_A^+$$ endowed with small parameter ϵ > 0. Through our choice of ϕ(ϵ, ·), we realize the situation that the perturbed system has a unique Gibbs measure μϵ of the potential ϕ(ϵ, ·) for each ϵ > 0 and on the other hand

更新日期：2020-01-17
• Isr. J. Math. (IF 0.764) Pub Date : 2020-01-17
Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa

We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field—assumed to be the real or the complex numbers—and which contains the field. Notably, we consider Fueter expansions, Gleason’s problem, the theory of hyperholomorphic rational functions, modules of Fueter series, and related problems. Such a framework includes many familiar algebras

更新日期：2020-01-17
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