Related papers: Are Banach spaces monadic?

We provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if $A\subseteq \mathbb{N}$ has positive Banach logarithmic density, then $A$ contains an approximate…

The absolute logarithmic Weil height is well defined on the group of units of the algebraic closure of the rational numbers, modulo roots of unity, and induces a metric topology on this group. We show that the completion of this metric…

It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banach spaces with the uniform approximation property. This generalizes a…

A topological space is said to be sequential if every sequentially closed subspace is closed. We consider Banach spaces with weak*-sequential dual ball. In particular, we show that if $X$ is a Banach space with weak*-sequentially compact…

We consider holomorphic semicocycles on the open unit ball in a Banach space taking values in a Banach algebra. We establish criteria for a semicocycle to be linearizable, that is, cohomologically equivalent to one independent of the…

Property($M$) in separable Banach spaces has played an important role in metric fixed point theory. This paper explores some of the Banach space properties that can be associated with Property($M$) and Property($M^*$).

Necessary and sufficient conditions for a separable Banach space to be a dual space are proved. Some applications are discussed

We study mean ergodic composition operators on infinite dimensional spaces of holomorphic functions of different types when defined on the unit ball of a Banach or a Hilbert space: that of all holomorphic functions, that of holomorphic…

In Euclidean spaces, every closed, bounded, convex set can be characterized by two equivalent notions of separation properties. This is not true in general for arbitrary Banach spaces. In this work, we present a ball separation…

We prove that Banach spaces $\ell_1\oplus_2\mathbb{R}$ and $X\oplus_\infty Y$, with strictly convex $X$ and $Y$, have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an…

We show that every metric space with bounded geometry uniformly embeds into an explicit reflexive Banach space (a direct sum of l^p spaces). In the case of discrete groups we show the analogue of a-T-menability. That is, we construct a…

We set up a descriptive set-theoretic framework to study Lipschitz-free spaces and use the reduction argument of Bossard to prove several results. We prove two universality results: if a separable Banach space is isomorphically universal…

We show that if X is a Banach space without cotype, then every locally finite metric space embeds metrically into X.

We give examples of real Banach spaces with exactly infinite countably many complex structures and with $\omega_1$ many complex structures.

We single out and study a natural class of Banach spaces -- almost square Banach spaces. In an almost square space we can find, given a finite set $x_1,x_2,\ldots,x_N$ in the unit sphere, a unit vector $y$ such that $\|x_i-y\|$ is almost…

In this working note we study the one-sided positive Banach-Mazur distance between some pairs of $C(K)$ Banach spaces. Building on methods developed in [4], we solve, in particular, one of the problems posed in [2].

Given two Banach function spaces we study the pointwise product space E.F, especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E . M(E, F)=F, where…

We first include a result of the second author showing that the Banach space S is complementably minimal. We then show that every block sequence of the unit vector basis of S has a subsequence which spans a space isomorphic to its square.…

The paper is concerned with b-metric and generalized b-metric spaces. One proves the existence of the completion of a generalized b-metric space and some fixed point results. The behavior of Lipschitz functions on b-metric spaces of…

In this note we study Banach spaces of traces of real polynomials on $\mathbb R^n$ to compact subsets equipped with supremum norms from the point of view of Geometric Functional Analysis.