Related papers: Are Banach spaces monadic?

In this paper we give necessary and sufficient conditions for the norm on an infinite dimensional Banach space to be sub differentiable, for various classes of Bananch spaces.

We study a local version of the ball-covering problem in Banach spaces, and obtain a complete solution to it in terms of the norm derivatives. We illustrate the advantage of the local approach by obtaining substantial refinements of several…

We call a closed subset M of a Banach space X a free basis of X if it contains the null vector and every Lipschitz map from M to a Banach space Y, which preserves the null vectors can be uniquely extended to a bounded linear map from X to…

We first unify all notions of partial injectivity appearing in the literature ---(universal) separable injectivity, (universal) $\aleph$-injectivity --- in the notion of $(\alpha, \beta)$-injectivity ($(\alpha, \beta)_\lambda$-injectivity…

We construct a complete metric space $M$ of cardinality continuum such that every non-singleton closed separable subset of $M$ fails to be a Lipschitz retract of $M$. This provides a metric analogue to the various classical and recent…

Given any Banach space $X$, let $L_2^X$ denote the Banach space of all measurable functions $f:[0,1]\to X$ for which ||f||_2:=(int_0^1 ||f(t)||^2 dt)^{1/2} is finite. We show that $X$ is a UMD--space (see \cite{BUR:1986}) if and only if…

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by…

In the context of classical associations between classes of Banach spaces and classes of compact Hausdorff spaces we survey known results and open questions concerning the existence and nonexistence of universal Banach spaces and of…

Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.

This is a survey of results on the classification of Banach spaces as metric spaces. It is based on a series of lectures I gave at the Functional Analysis Seminar in 1984-1985, and it appeared in the 1984-1985 issue of the Longhorn Notes. I…

In this paper, we continue our study of quasihyperbolic metric in Banach spaces. The main results of the paper present a criterion for smoothness of geodesics of quasihyperbolic type metrics in Banach spaces, under a Dini type condition on…

We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…

This paper brings new results on the FPP in Banach spaces $X$ with a Schauder basis. We first deal with the problem of whether there is a Banach space isomorphic to $\co$ having the FPP. We show that the answer is negative if $X$ contains a…

In the past few decades, much has been done regarding the descriptive set theory of separable Banach spaces. However, the descriptive properties of separable Fr\'echet spaces have not yet been investigated. In these notes, we look at this…

The article presents a new method of integration of functions with values in Banach spaces. This integral and related notions prove to be a useful tool in the study of Banach space geomtry.

In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…

We study the way in which the Euclidean subspaces of a Banach space fit together, somewhat in the spirit of the Ka\v{s}in decomposition. The main tool that we introduce is an estimate regarding the convex hull of a convex body in John's…

State monads in cartesian closed categories are those defined by the familiar adjunction between product and exponential. We investigate the structure of their algebras, and show that the exponential functor is monadic provided the base…

We settle several questions regarding the model theory of Nakano spaces left open by the PhD thesis of Pedro Poitevin \cite{Poitevin:PhD}. We start by studying isometric Banach lattice embeddings of Nakano spaces, showing that in dimension…

We give a streamlined proof of the multiplicative ergodic theorem for quasi-compact operators on Banach spaces with a separable dual.