Related papers: Function spaces not containing $\ell_{1}$

This article, addressed to a general audience of functional analysts, is intended to be an illustration of a few basic principles from `noncommutative functional analysis', more specifically the new field of {\em operator spaces.} In our…

We introduce a new class $\mathcal{FV}(\Omega,E)$ of spaces of weighted functions on a set $\Omega$ with values in a locally convex Hausdorff space $E$ which covers many classical spaces of vector-valued functions like continuous, smooth,…

We introduce Omega functions that generalize Euler Gamma functions and study the functional difference equation they satisfy. Under a natural exponential growth condition, the vector space of meromorphic solutions of the functional equation…

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 generalize an important class of Banach spaces, namely the $M$-embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided $M$-embedded operator spaces are the operator spaces which are one-sided $M$-ideals…

Let $n \geq 4$ and let $\Omega$ be a bounded hyperconvex domain in $\mathbb{C}^{n}$. Let $\varphi$ be a negative exhaustive smooth plurisubharmonic function on $\Omega$. We show that any holomorphic function defined on a connected open…

As objects of study in functional analysis, Hilbert spaces stand out as special objects of study as do nuclear spaces in view of a rich geometrical structure they possess as Banach and Frechet spaces, respectively. On the other hand, there…

Let $\lambda$ be a large enough cardinal number (assuming GCH it suffices to let $\lambda=\aleph_\omega$). If $X$ is a Banach space with $\text{dens}(X)\ge\lambda$, which admits a coarse (or uniform) embedding into any $c_0(\Gamma)$, then…

An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree $\mathcal T$ of a certain type on a space X is…

We prove that every continuous function $f:E\to Y$ depends on countably many coordinates, if $E$ is an $(\aleph_1,\aleph_0)$-invariant pseudo-$\aleph_1$-compact subspace of a product of topological spaces and $Y$ is a space with a regular…

We investigate the reflexivity of the isometry group and the automorphism group of some important metric linear spaces and algebras. The paper consists of the following sections: 1. Preliminaries. 2. Sequence spaces. 3. Spaces of measurable…

We construct an indecomposable reflexive Banach space $X_{ius}$ such that every infinite dimensional closed subspace contains an unconditional basic sequence. We also show that every operator $T\in \mathcal{B}(X_{ius})$ is of the form…

We show that any Banach space contains a continuum of non isomorphic subspaces or a minimal subspace. We define an ergodic Banach space $X$ as a space such that $E_0$ Borel reduces to isomorphism on the set of subspaces of $X$, and show…

In this note we show that every Banach space $X$ not containing $\ell_1^n$ uniformly and with unconditional basis contains an arbitrarily distortable subspace.

Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators with constant coefficients on $\mathbb{T}^2$ and the space of smooth functions generated by this collection, namely, the space of functions $f$ such that $T_j f…

Let Omega subset of C^d be an open set and Km, m = 1, 2, . . . an exhaustion of Omega by compact subsets of Omega. We set Omega_m = int(Km) and let Xm(Omega_m) be a topological space of holomorphic functions on Omega_m between A^ infinity…

Let $\Gamma$ be an infinite set equipped with the discrete topology. We prove that the space $\ell_{\infty}(\Gamma),$ of all complex-valued bounded functions on $\Gamma$, satisfies the Mazur-Ulam property, that is, every surjective isometry…

We characterize the class of separable Banach spaces $X$ such that for every continuous function $f:X\to\mathbb{R}$ and for every continuous function $\epsilon:X\to\mathbb(0,+\infty)$ there exists a $C^1$ smooth function $g:X\to\mathbb{R}$…

In 1970 Haskell Rosenthal proved that if $X$ is a Banach space, $\Gamma$ is an infinite index set, and $T:\ell_\infty(\Gamma)\to X$ is a bounded linear operator such that $\inf_{\gamma\in\Gamma}\|T(e_\gamma)\|>0$ then $T$ acts as an…

We show that several spaces of holomorphic functions on a Riemann domain over a Banach space, including the nuclear and Hilbert-Schmidt bounded type, are locally $m$-convex Fr\'echet algebras. We prove that the spectrum of these algebras…