Related papers: Banach spaces with projectional skeletons

the main goal of this paper is to prove that any Banach space X, that every dual ball in X** is weak* -separable, or every weak* -closed convex subset in X** is weak* -separable, or every norm-closed convex set in X* is constructible,…

We study Banach spaces whose group of isometries acts micro-transitively on the unit sphere. We introduce a weaker property, which one-complemented subspaces inherit, that we call uniform micro-semitransitivity. We prove a number of results…

We show that the description of the holomorphic $\mathbb C \mathrm P^1$-bundle associated to a holomorphic projective structure on a Riemann surface in terms of the principal bundle of projective $2$-frames extends very well to the setting…

Hereditarily indecomposable Banach spaces may have density at most continuum (Plichko-Yost, Argyros-Tolias). In this paper we show that this cannot be proved for indecomposable Banach spaces. We provide the first example of an…

It is known that a Banach space contains an isomorphic copy of $c_0$ if, and only if, it can be equivalently renormed to be almost square. We introduce and study transfinite versions of almost square Banach spaces with the purpose to relate…

Metric projection operators can be defined in similar wayin Hilbert and Banach spaces. At the same time, they differ signifitiantly in their properties. Metric projection operator in Hilbert space is a monotone and nonexpansive operator. It…

This note has two objectives. The first objective is show that, even if a separable Banach space does not have a Schauder basis (S-basis), there always exists Hilbert spaces $\mcH_1$ and $\mcH_2$, such that $\mcH_1$ is a continuous dense…

For a Banach space $X$ with a shrinking Schauder frame $(x_i,f_i)$ we provide an explicit method for constructing a shrinking associated basis. In the case that the minimal associated basis is not shrinking, we prove that every shrinking…

Consider a Berkovich space over a good Banach ring and the relative projective line over it. (It is a space whose fibers are projective lines over different complete valued fields.) For each polarized endomorphism of this line, we prove…

Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X. Let Pc from X to C denote the (standard) metric projection operator. In this paper, we define the Gateaux directional…

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…

For each ordinal $\alpha< \omega_1$, we prove the existence of a separable, reflexive Banach space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of separable, reflexive Banach spaces $X$ such that the…

A display of a topological group G on a Banach space X is a topological isomorphism of G with the isometry group Isom(X,||.||) for some equivalent norm ||.|| on X, where the latter group is equipped with the strong operator topology.…

In this paper, we prove the following results. There exists a Banach space without basis which has a Schauder frame. There exists an universal Banach space $B$ (resp. $\tilde{B}$) with a basis (resp. an unconditional basis) such that, a…

We prove some results on weakly almost square Banach spaces and their relatives. On the one hand, we discuss weak almost squareness in the setting of Banach function spaces. More precisely, let $(\Omega,\Sigma)$ be a measurable space, let…

A separable Banach space $X$ is said to be finitely determined if for each separable space $Y$ such that $X$ is finitely representable (f.r.) in $Y$ and $Y$ is f.r. in $X$ then $Y$ is isometric to $X$. We provide a direct proof (without…

We study the general measures of non-compactness defined on subsets of a dual Banach space, their associated derivations and their $\omega$-iterates. We introduce the notions of convexifiable and sublinear measure of non-compactness and…

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…

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…

We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are {\it rigged sequences spaces}, Banach spaces of sequences, with…