Related papers: Some Banach algebra structures for l^p({\beta}) an…

We show that if the Hilbert transform with values in a Banach space is $L^p$ bounded, then so is the dyadic Hilbert transform, with a linear relation of the norms.

The study of operator algebras on Hilbert spaces, and C*-algebras in particular, is one of the most active areas within Functional Analysis. A natural generalization of these is to replace Hilbert spaces (which are $L^2$-spaces) with…

We analyze a definition of product of Banach spaces that is naturally associated by duality with an abstract notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different…

For a nontrivial locally compact group $G$, and $p\in [1,\infty)$, consider the Banach algebras of $p$-pseudofunctions, $p$-pseudomeasures, $p$-convolvers, and the full group $L^p$-operator algebra. We show that these Banach algebras are…

We show that the $\ell^p$-pseudofunctions, which were recently shown to lead to exotic completions of group $C^*$-algebras by Wiersma and the second named author, can be used to construct well-behaved crossed product functors in the sense…

We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincar\'e duality and hard Lefschetz theorem), and their relations and applications to integral…

Although the Bergman projection operator $\mathbf{B}_{\Omega}$ is defined on $L^2(\Omega)$, its behavior on other $L^p(\Omega)$ spaces for $p\not =2$ is an active research area. We survey some of the recent results on $L^p$ estimates on the…

Can polynomial interpolation be extended to a Banach space setting? Are tensors whose elements are non-commutative Banach space elements legitimate objects with notable analytic and algebraic properties? Here we explore these questions and…

We analyze the spectra of generalized Fibonacci and Fibonacci-like operators in Banach space $l^1$. Some of the results have application in population dynamics.

For each $1\le p<\infty$ and each countable directed graph $E$ we consider the Leavitt path $\mathbb{C}$-algebra $L(E)$ and the $L^p$-operator graph algebra $\mathcal{O}^p(E)$. We show that the (purely infinite) simplicity of…

A generalized notion of a Lie algebroid is presented. Using this, the Lie algebroid generalized tangent bundle is obtained. A new point of view over (linear) connections theory on a fiber bundle is presented. These connections are…

This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…

We construct for each $0<p\le 1$ an infinite collection of subspaces of $\ell_p$ that extend the example from [J. Lindenstrauss, On a certain subspace of $\ell_{1}$, Bull. Acad. Polon. Sci. S\'er. Sci. Math. Astronom. Phys. 12 (1964),…

Bounded and compact generalized weighted composition operators acting from the weighted Bergman space $A^p_\omega$, where $0<p<\infty$ and $\omega$ belongs to the class $\mathcal{D}$ of radial weights satisfying a two-sided doubling…

Given any square matrix or a bounded operator $A$ in a Hilbert space such that $p(A)$ is normal (or similar to normal), we construct a Banach algebra, depending on the polynomial $p$, for which a simple functional calculus holds. When the…

In this paper we find some necessary and sufficient conditions for a Banach algebra to be amenable or weakly amenable, by applying the homomorphisms on Banach algebras.

We generalize earlier results about connected components of idempotents in Banach algebras, due to B. Sz\H{o}kefalvi Nagy, Y. Kato, S. Maeda, Z. V. Kovarik, J. Zem\'anek, J. Esterle. Let $A$ be a unital complex Banach algebra, and…

In this paper structure of infinite dimensional Banach spaces is studied by using an asymptotic approach based on stabilization at infinity of finite dimensional subspaces which appear everywhere far away. This leads to notions of…

Let $A$ be a commutative semisimple Banach algebra, $X$ be a locally compact Hausdorff topological space and $G$ be a locally compact topological group. In this paper, we investigate several properties of vector valued Banach algebras…

Motivated by a question of Vincent Lafforgue, we study the Banach spaces $X$ satisfying the following property: there is a function $\vp\to \Delta_X(\vp)$ tending to zero with $\vp>0$ such that every operator $T\colon L_2\to L_2$ with…