Related papers: Weighted inversion of vector valued Dirichlet seri…

We study Johnson amenability for unconditional direct sums of Banach algebras. Given a family $(A_i)_{i\in I}$ of Banach algebras and a Banach sequence lattice $E$ on~$I$, the $E$-sum $\bigl(\bigoplus_{i\in I} A_i\bigr)_{\!E}$ carries a…

We show that if the Szlenk index of a Banach space $X$ is larger than the first infinite ordinal $\omega$ or if the Szlenk index of its dual is larger than $\omega$, then the tree of all finite sequences of integers equipped with the…

In this note, given a pair $(\mathfrak{g}, \lambda)$, where $\mathfrak{g}$ is a complex semisimple Lie algebra and $\lambda \in \mathfrak{h}^*$ is a dominant integral weight of $\mathfrak{g}$, where $\mathfrak{h} \subset \mathfrak{g}$ is…

For a Banach algebra $ \mathcal{A} $, we introduce various approximate virtual diagonals such as approximate WAP-virtual diagonal and approximate virtual diagonal. For the enveloping dual Banach algebra $ F(\mathcal{A}) $ of $ \mathcal{A}…

Let $\fg$ be any untwisted affine Kac-Moody algebra, $\mu$ any fixed complex number, and $\wt\fg(\mu)$ the corresponding toroidal extended affine Lie algebra of nullity two. For any $k$-tuple $\bm{\lambda}=({\lambda}_1, \cdots,…

We establish a closed formula for a singular vector of weight $\lambda-\beta$ in the Verma module of highest weight $\lambda$ for Lie superalgebra $\mathfrak{gl}(m|n)$ when $\lambda$ is atypical with respect to an odd positive root $\beta$.…

Let $A$ be a commutative Banach algebra and $X$ be a compact space. The class of Banach $A$-valued function algebras on $X$ consists of subalgebras of $C(X,A)$ with certain properties. We introduce the notion of $A$-characters on an…

An algebra of bounded linear operators on a Banach space is said to be {\em strongly compact} if its unit ball is precompact in the strong operator topology, and a bounded linear operator on a Banach space is said to be {\em strongly…

Let $A$ and $B$ be Banach algebras and let $B$ be an algebraic Banach $A-$bimodule. Then the $\ell^1-$direct sum $A\times B$ equipped with the multiplication $$(a_1,b_1)(a_2,b_2)=(a_1a_2,a_1\cdot b_2+b_1\cdot a_2+b_1b_2),~~ (a_1, a_2\in A,…

In this paper we study weighted versions of Fourier algebras of compact quantum groups. We focus on the spectral aspects of these Banach algebras in two different ways. We first investigate their Gelfand spectrum, which shows a connection…

It is a well-known fact in K-theory that the rapidly decreasing matrices of countable size form an associative topological algebra whose set of quasi-invertible elements is open, and such that the quasi-inversion map is continuous. We…

Here we consider two algebras, a free unital associative complex algebra (denoted by ${\mathcal{B}}$) equiped with a multiparametric \textbf{\emph{q}}-differential structure and a twisted group algebra (denoted by ${\mathcal{A}(S_{n})}$),…

A Banach algebra A is self-induced if the multiplication is an isomorphism from the A-balanced projective tensor-square of A to A. The class of self-induced Banach algebras is a natural generalization of unital Banach algebras, providing a…

In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an $\alpha$-inverse-strongly…

We present quantitative versions of Bohr's theorem on general Dirichlet series $D=\sum a_{n} e^{-\lambda_{n}s}$ assuming different assumptions on the frequency $\lambda:=(\lambda_{n})$, including the conditions introduced by Bohr and…

Let $\mathbb{H}$ be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on $L^{p}(\mathbb{H})$, given by the off-diagonal decay of the kernel. As a consequence of…

Given an action $\varphi$ of of inverse semigroup $S$ on a ring $A$ (with domain of $\varphi(s)$ denoted by $D_{s^*}$) we show that if the ideals $D_e$, with $e$ an idempotent, are unital, then the skew inverse semigroup ring $A\rtimes S$…

Let $\mathfrak{g}$ be a finite-dimensional simple complex Lie algebra. A layer sum is introduced as the sum of formal exponentials of the distinct weights appearing in an irreducible $\mathfrak{g}$-module. It is argued that the character of…

The Matrix Bochner Problem aims to classify weight matrices $W$ such that the algebra $\mathcal D(W)$, of all differential operators that have a sequence of matrix-valued orthogonal polynomials for $W$ as eigenfunctions, contains a…

Given a Banach space $A$ and fix a non-zero $\varphi\in A^*$ with $\|\varphi\|\leq 1$. Then the product $a\cdot b=\langle\varphi, a\rangle\ b$ turning $A$ into a Banach algebra which will be denoted by $_\varphi A.$ Some of the main…