Related papers: Convex-Cyclic Weighted Translations On Locally Com…

Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…

Let $\mathbb{G}$ be a locally compact abelian group and let $1<p\leq 2$. $\mathbb{G}^{'}$ is the dual group of $\mathbb{G}$, and $p^{'}$ the conjugate exponent of $p$. An operator $T$ between Banach spaces $X$ and $Y$ is said to be…

This article aims to initiate a study of bilateral weighted backward shift operators defined on the spaces $\ell^p_{a,b}(\Omega_{r,R})$ and $c_{0,a,b}(\Omega_{r,R})$ which are Banach spaces of analytic functions on a suitable annulus in the…

We show that every hypercyclic operator on a real locally convex space admits a dense, invariant linear manifold of hypercyclic vectors.

Let $G$ be a discrete group, let $p\ge1$, and let $\omega$ be a weight on $G$. Using the approach from [9], we provide sufficient conditions on a weight $\omega$ for $\ell^p(G,\omega)$ to be a Banach algebra admitting a norm-controlled…

We first generalize the results of Le\'on and M\"uller [Studia Math. 175(1) 2006] on hypercyclic subspaces to sequences of operators on Fr\'echet spaces with a continuous norm. Then we study the particular case of iterates of an operator T…

Let $(T\_\lambda)\_{\lambda\in\Lambda}$ be a family of operators acting on a $F$-space $X$, where the parameter space $\Lambda$ is a subset of $\mathbb R^d$. We give sufficient conditions on the family to yield the existence of a vector…

It is well known that under certain conditions on a Banach space $X$, the set of bounded linear operators attaining their numerical radius is a dense subset. We prove in this paper that if $X$ is assumed to be uniformly convex and uniformly…

A continuous operator $T$ between two Banach lattices $E$ and $F$ is called almost order-weakly compact, whenever for each almost order bounded subset $A$ of $E$, $T(A)$ is a relatively weakly compact subset of $F$. In Theorem 4, we show…

A bounded linear operator $T$ on a separable complex Hilbert space $H$ is called $C$-normal if there is a conjugation $C$ on $H$ such that $ CT^\ast TC=TT^\ast$. Let $\varphi$ be a linear fractional self-map of $\mathbb{D}$. In this paper,…

For a Polish group G let cov_G be the minimal number of translates of a fixed closed nowhere dense subset of G required to cover G. For many locally compact G this cardinal is known to be consistently larger than cov(meager) which is the…

Convex geometry is a closure space $(G,\phi)$ with the anti-exchange property. A classical result of Edelman and Jamison (1985) claims that every finite convex geometry is a join of several linear sub-geometries, and the smallest number of…

In the present note we introduce tame functionals on Banach algebras. A functional $f \in A^*$ on a Banach algebra $A$ is tame if the naturally defined linear operator $A \to A^*, a \mapsto f \cdot a$ factors through Rosenthal Banach spaces…

The main goal of this paper is to prove a two-weight criteria for multidimensio-nal Hardy type operator from weighted Lebesgue spaces into $p$-convex weighted Banach function spaces. Analogously problem for the dual operator is considered.…

We extend a result of B\`{e}s, Martin, Peris and Shkarin by stating: $B_w$ is $\mathscr{F}$-weighted backward shift if and only if $(B_w,\dots, B_w^r)$ is $d$-$\mathscr{F}$, for any $r\in \mathbb{N}$, where $\mathscr{F}$ runs along some…

In a recent article (2022) we proved with L. Zaj\'i\v{c}ek that if $ G\subset\R^n $ is an unbounded open convex set that does not contain a translation of a convex cone with non-empty interior, then there exist $ f:G\to\R $ and a concave…

We study infinite matrices $A$ indexed by a discrete group $G$ that are dominated by a convolution operator in the sense that $|(Ac)(x)| \leq (a \ast |c|)(x)$ for $x\in G$ and some $a\in \ell ^1(G)$. This class of "convolution-dominated"…

Let $A$ be a bounded linear operator on a complex Banach space $X.$ For a given $\alpha \geq 0,$ we consider the class $\mathcal{D}_{A}^{\alpha }\left( \mathbb{R} \right) $ of all bounded linear operators $T$ on $X$ for which there exists a…

We show that if the Hardy-Littlewood maximal operator is bounded on a reflexive Banach function space $X(\mathbb{R})$ and on its associate space $X'(\mathbb{R})$, then the space $X(\mathbb{R})$ has an unconditional wavelet basis. As a…

Let ${\Bbb G}$ be a locally compact quantum group and ${\mathcal T}(L^2({\Bbb G}))$ be the Banach algebra of trace class operators on $L^2({\Bbb G})$ with the convolution induced by the right fundamental unitary of ${\Bbb G}$. We study the…