Related papers: On Banach Spaces with the Helly Approximation Prop…

Following Davie's example of a Banach space failing the approximation property [D], we show how to construct a Banach space E which is asymptotically Hilbertian and fails the approximation property. Moreover, the space E is shown to be a…

A Banach space X has the average distance property (ADP) if there exists a unique real number r such that for each positive integer n and all x_1,...,x_n in the unit sphere of X there is some x in the unit sphere of X such that 1/n…

We prove the symmetric version of Kottman's theorem, that is to say, we demonstrate that the unit sphere of an infinite-dimensional Banach space contains an infinite subset $A$ with the property that $\|x\pm y\| > 1$ for distinct elements…

The purpose of this paper is to lay the foundations for the study of the problem of when $\Ext^n(X, Y)=0$ in Banach/quasi-Banach spaces. We provide a number of examples of couples $X,Y$ so that $\Ext^n(X,Y)$ is (or is not ) $0$, including…

We deal with isomorphic Banach-Stone type theorems for closed subspaces of vector-valued continuous functions. Let $\mathbb{F}=\mathbb{R}$ or $\mathbb{C}$. For $i=1,2$, let $E_i$ be a reflexive Banach space over $\mathbb{F}$ with a certain…

A necessary and sufficient condition for existence of a Banach space with a finite dimensional decomposition but without the $\pi$-property in terms of norms of compositions of projections is found.

Let X and Y be two infinite-dimensional Banach spaces. If X is crudely finitely representable in every finite-codimensional subspace of Y, then any proper subset of X almost bi-Lipschitz embeds into Y, in a sense quite close to that of F.…

Naor and Mendel's metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz equivalent to an…

The main result of this paper states that if a Banach space X has the property that every bounded operator from an arbitrary subspace of X into an arbitrary Banach space of cotype 2 extends to a bounded operator on X, then…

The main result of this paper is that every non-reflexive subspace $Y$ of $L_1[0,1]$ fails the fixed point property for closed, bounded, convex subsets $C$ of $Y$ and nonexpansive (or contractive) mappings on $C$. Combined with a theorem of…

For any $n\ge 2$, $\Omega\subset\rn$, and any given convex and coercive Hamiltonian function $H\in C^{0}(\rn)$, we find an optimal sufficient condition on $H$, that is, for any $c\in\mathbb R$, the level set $H^{-1}(c)$ does not contains…

The Khinchin-Kahane inequality is a fundamental result in the probability literature, with the most general version to date holding in Banach spaces. Motivated by modern settings and applications, we generalize this inequality to arbitrary…

We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations…

We study the set $\operatorname{MA}(X,Y)$ of operators between Banach spaces $X$ and $Y$ that attain their minimum norm, and the set $\operatorname{QMA}(X,Y)$ of operators that quasi attain their minimum norm. We characterize the…

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 this paper, we introduce the notion of topologically Banach contraction mapping defined on an arbitrary topological space X with the help of a continuous function $g:X\times X\rightarrow \mathbb{R}$ and investigate the existence of fixed…

In [2] we characterized in terms of a quadratic growth condition various metric regularity properties of the subdifferential of a lower semicontinuous convex function acting in a Hilbert space. Motivated by some recent results in [16] where…

We show that, as conjectured by Adrien Douady back in 1972, every complete metric space is homeomorphic (moreover, isometric) to the locus of zeros of an analytic map between two Banach spaces. As a corollary, a paracompact topological…

Let $X$ be a weakly pseudoconvex manifold and $L\longrightarrow X$ be a holomorphic line bundle with a singular positive Hermitian metric $h$. In this article, we provide a points separation theorem and an embedding for the adjoint linear…

In this paper we give some results about the approximation of a Lipschitz function on a Banach space by means of $\Delta$-convex functions. In particular, we prove that the density of $\Delta$-convex functions in the set of Lipschitz…