Related papers: Simultaneous power factorization in modules over B…

The parallel sum $A:B$ of two bounded positive linear operators $A,B$ on a Hilbert space $H$ is defined to be the positive operator having the quadratic form \begin{equation*} \inf\{(A(x-y)\,|\,x-y)+(By\,|\,y)\,|\,y\in H\} \end{equation*}…

We give a criterion ensuring that the elementary class of a modular Banach space E (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of E) consists of all direct sums E\oplus_m H, where H…

For a Banach left module action, we will extend some propositions from Lau and $\ddot{U}$lger and others into general situations and we establish the relationships between topological centers of the left module action with the multiplier…

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 consider several notions of regularity, including strong regularity, bounded relative units, and Ditkin's condition, in the setting of vector-valued function algebras. Given a commutative Banach algebra $A$ and a compact space $X$, let…

Let $X$ be a compact Hausdorff space and $A$ a Banach algebra. We investigate amenability properties of the algebra $C(X,A)$ of all $A$-valued continuous functions. We show that $C(X,A)$ has a bounded approximate diagonal if and only if $A$…

The main goal of this paper is to characterize arbitrary nonlinear (non-multilinear) mappings $f:X_{1}\times...\times X_{n}\rightarrow Y$ between Banach spaces that satisfy a quite natural Pietsch Domination-type theorem around a given…

In earlier work a crossed product of a Banach algebra was constructed from a Banach algebra dynamical system $(A,G,\alpha)$ and a class $\mathcal{R}$ of continuous covariant representations, and its representations were determined. In this…

We present a way to turn an arbitrary (unbounded) metric space $\mathcal{M}$ into a bounded metric space $\mathcal{B}$ in such a way that the corresponding Lipschitz-free spaces $\mathcal{F}(\mathcal{M})$ and $\mathcal{F}(\mathcal{B})$ are…

The framework of the paper is that of the full Fock space ${\Cal F}^2({\Cal H}_n)$ and the Banach algebra $F^\infty$ which can be viewed as non-commutative analogues of the Hardy spaces $H^2$ and $H^\infty$ respectively. An inner-outer…

In this paper, methods of second order and higher order reverse mathematics are applied to versions of a theorem of Banach that extends the Schroeder-Bernstein theorem. Some additional results address statements in higher order arithmetic…

The purpose of this paper is to characterize several classes of functional identities involving inverses with related mappings from a unital Banach algebra $\mathcal{A}$ over the complex field into a unital $\mathcal{A}$-bimodule…

The conditions on a Banach space, $E$, under which the algebra, $\mathcal{K}(E)$, of compact operators on $E$ is right flat or homologically unital are investigated. These homological properties are related to factorization in the algebra…

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…

The main purpose of this paper is the study of a~new class of summing multilinear operators acting from the product of Banach lattices with some nontrivial lattice convexity. A~mixed Pietsch-Maurey-Rosenthal type factorization theorem for…

Let $X(\mathbb{R})$ be a separable Banach function space such that the Hardy-Littlewood maximal operator is bounded $X(\mathbb{R})$ and on its associate space $X'(\mathbb{R})$. The algebra $C_X(\dot{\mathbb{R}})$ of continuous Fourier…

We present a general method to extend results on Hilbert space operators to the Banach space setting by representing certain sets of Banach space operators $\Gamma$ on a Hilbert space. Our assumption on $\Gamma$ is expressed in terms of…

Let $X$ be a real normed vector space with a cone $K\subseteq X$ satisfying either (i) $K$ is closed with non-empty interior or (ii) $K$ has non-zero extremals or (iii) $K$ is closed and $X$ is a Banach space. In this short note, we provide…

Let X be a complex Banach space of dimension at least 2, and let S be a multiplicative semigroup of operators on X such that the rank of AB - BA is at most 1 for all pairs {A,B} in S. We prove that S has a non-trivial invariant subspace…

Let X be a Hilbert bimodule over a C*-algebra A and $O_X= A \rtimes_X \Z$. Using a finite section method we construct a sequence of completely positive contractions factoring through matrix algebras over A which act on $s_{\xi} s_{\eta}^*$…