Related papers: Weakly almost periodic functionals, representation…

We give a new proof of the "weakly admissible implies admissible" theorem of Colmez and Fontaine describing the semi-stable p-adic representations. We study Banach-Colmez spaces, i.e. p-adic Banach spaces with the extra data of a…

In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space,…

We study a class of left-invertible operators which we call weakly concave operators. It includes the class of concave operators and some subclasses of expansive strict $m$-isometries with $m > 2$. We prove a Wold-type decomposition for…

We describe a weak tracial analog of approximate representability under the name "weak tracial approximate representability" for finite group actions. Let $G$ be a finite abelian group, let $A$ be an infinite-dimensional simple unital…

In this paper, we characterize supercyclic weighted composition operators on a large class of solid Banach function spaces, in particular on Lebesgue, Orlicz and Morrey spaces. Also, we characterize supercyclic weighted composition…

We introduce an equivariant version of the weak expectation property (WEP) at the level of operator modules over completely contractive Banach algebras $A$. We prove a number of general results---for example, a characterization of the…

By a result of Johnson, the Banach space $F=(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_\infty}$ contains a complemented copy of $\ell_1$. We identify $F$ with a complemented subspace of the space of (bounded, linear) operators on the reflexive…

Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…

We prove some results on weakly almost square Banach spaces and their relatives. On the one hand, we discuss weak almost squareness in the setting of Banach function spaces. More precisely, let $(\Omega,\Sigma)$ be a measurable space, let…

We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to $\mathbb{Z}_2^n$ (also negative values of the multiplicity function are…

Let $A$ be a Banach algebra with a bounded left approximate identity $\{e_\lambda\}_{\lambda\in\Lambda}$, let $\pi$ be a continuous representation of $A$ on a Banach space $X$, and let $S$ be a non-empty subset of $X$ such that…

The question which led to the title of this note is the following: {\it If $X$ is a Banach space and $K$ is a compact subset of $X$, is it possible to find a compact, or even approximable, operator $v:X\to X$ such that…

We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator…

In this paper, equivalence between interpolation properties of linear operators and monotonicity conditions are studied, for a pair $(X_0,X_1)$ of rearrangement invariant quasi Banach spaces, when the extreme spaces of the interpolation are…

Well-bounded operators are linear operators on a Banach space $X$ that have an $AC[a,b]$ functional calculus for some interval $[a,b]$. A well-bounded operator is of type (B) if it can be written as an integral against a spectral family of…

We have derived that on certain Banach spaces having a graph structure $G$, the iterations for asymptotically $G$-nonexpansive map will converge weakly towards a fixed point. This result unifies and extends several theorems on fixed points…

We prove weak and strong convergence theorems for a double Krasnoselskij type iterative method to approximate coupled solutions of a bivariate nonexpansive operator F : C x C --> C, where C is a nonempty closed and convex subset of a…

We show that every Banach space in which weakly compact sets are super weakly compact in automatically weakly sequentially complete answering a question by Silber (2024). In the proof we show how to build a weakly compact set which is not…

We prove collective versions of semi-duality theorems for sets of almost (limitedly, order) L-weakly compact operators.

We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this…