Related papers: Reflexive Cones
In this paper, we study the coarse Lipschitz geometry of Banach spaces with several asymptotic properties. Specifically, we look at asymptotically uniformly smoothness and convexity, and several distinct Banach-Saks-like properties. Among…
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 investigate possible quantifications of the Banach-Saks property and the weak Banach-Saks property. We prove quantitative versions of relationships of the Banach-Saks property of a set with norm compactness and weak compactness. We…
A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the…
We prove in this short report that for arbitrary weak converging sequence of sigma-finite Borelian measures in the separable Banach space there is a compact embedded separable subspace such that this measures not only are concentrated in…
Motivated by the equivalent definition of a continuous operator between Banach spaces in terms of weakly null nets, we introduce two types of continuous operators between Banach lattices using unbounded absolute weak convergence. We…
Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to…
A Banach space is locally almost square if, for every $y$ in its unit sphere, there exists a sequence $(x_n)$ in its unit sphere such that $\lim\|y\pm x_n\|=1$. A Banach space is weakly almost square if, in addition, we require the sequence…
We extend to Banach space nest algebras the theory of essential supports and support function pairs of their bimodules, thereby obtaining Banach space counterparts of long established results for Hilbert space nest algebras. Namely, given a…
In this note, we consider several notions related to the Grothendieck property. Among them, we introduce the notion "unbounded Grothendieck property" in a Banach lattice as an unbounded version of the known Grothedieck property in the…
We present a new proof of Zippin's Embedding Theorem, that every separable reflexive Banach space embeds into one with shrinking and boundedly complete basis, and every Banach space with a separable dual embeds into one with a shrinking…
In this work we study three different versions of small diameter properties of the unit ball in a Banach space and its dual. The related concepts for all closed bounded convex sets of a Banach space was initiated and developed in \cite{B3},…
For a countable ordinal a we denote by C_a the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by a. We show that each C_a admits a separable, reflexive universal space. We also…
In this note, we study the geometry of the unit ball of the Banach space generated by the adequate family of all subsets of branches of the infinite binary tree, and answer several open questions related to slicely countably determined…
We study Banach spaces with a weak stable unit ball, that is Banach spaces where every convex combination of relatively weakly open subsets in its unit ball is again a relatively weakly open subset in its unit ball. It is proved that the…
A Banach space $X$ is reflexive if the Mackey topology $\tau(X^*,X)$ on $X^*$ agrees with the norm topology on $X^*$. Borwein [B] calls a Banach space $X$ {\it sequentially reflexive\/} provided that every $\tau(X^*,X)$ convergent {\it…
We show that warped cones over actions with spectral gaps do not embed coarsely into large classes of Banach spaces. In particular, there exist warped cones over actions of the free group that do not embed coarsely into $L_p$-spaces and…
We introduce and study two notions of entropy in a Banach space X with a normalized Schauder basis . The geometric entropy E(A) of a subset A of X is defined to be the infimum of radii of compact bricks containing A. We obtain several…
The method of compatible sequences is introduced in order to produce non-trivial (closed) invariant subspaces of (bounded linear) operators. Also a topological tool is used which is new in the search of invariant subspaces: the extraction…
Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…