Related papers: On the c_0-extension property

The Erberlein-Smulian Theorem asserts that for complete normed spaces, that is Banach spaces, a subset is weak compact if and only if it is weak sequentially compact. In this paper it is shown that the completeness of the normed space is…

We investigate for a bounded semigroup of linear operators $S$ on a Banach space $E$ and a vector $x \in E$, when relative compactness of $S(I-T)x$ for every $T \in S$ implies relative compactness of the orbit $Sx$. In particular, we derive…

For any complex Banach space $X$, let $J$ denote the duality mapping of $X$. For any unit vector $x$ in $X$ and any ($C_0$) contraction semigroup $(T_t)_{t>0}$ on $X$, Baillon and Guerre-Delabriere proved that if $X$ is a smooth reflexive…

In this paper, we consider the question of contractivity vs. complete contractivity for domains in $\mathbb{C}^2$, which are unit balls with respect to some norm. We show that for a large class of Reinhardt domains, the corresponding Banach…

We will introduce the countable separation property (CSP) of Banach spaces X, which is defined as follows: For each subset \mathcal{F} of X^{\ast}, which separates X, there exists a countable separating subset \mathcal{F}_{0} of…

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. Then we prove that a separable reflexive Banach space with the unconditional tree…

Following [3] we say that a Tychonoff space $X$ is an Ascoli space if every compact subset $\mathcal{K}$ of $C_k(X)$ is evenly continuous; this notion is closely related to the classical Ascoli theorem. Every $k_\mathbb{R}$-space, hence any…

These notes are dedicated to the study of the complexity of several classes of separable Banach spaces. We compute the complexity of the Banach-Saks property, the alternating Banach-Saks property, the complete continuous property, and the…

Motivated by weak null singularities in black hole interiors, we study 1+1 dimensional Lorentzian manifolds $(M,g)$ which admit a continuous spacetime extension across a null boundary $v=0$, where $v<0$ is a null coordinate. We study the…

This paper deals with the problem of when, given a collection $\mathcal C$ of weakly compact operators between separable Banach spaces, there exists a separable reflexive Banach space $Z$ with a Schauder basis so that every element in…

We prove an implicit function theorem for C^k-maps from arbitrary topological vector spaces over valued fields to Banach spaces (for k at least 2). As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of…

The problem involving the extension of functions from a certain class and defined on subdomains of the ambient space to the whole space is an old and a well investigated theme in analysis. A related question whether the extensions that…

The Kasner spacetime is a cosmological model of an anisotropic expanding universe without matter and is an exact solution of the Einstein vacuum equations Ric(g) = 0. It is manifestly inextendible as a Lorentzian manifold with a twice…

We prove two theorems about differentiable functions on the Banach space C(K), where K is compact. (i) If C(K) admits a non-trivial function of class C^m and of bounded support, then all continuous real-valued functions on C(K) may be…

We show that if a separable Banach space has Kalton's property $(M^\ast)$, then all $\varepsilon$-Szlenk derivations of the dual unit ball are balls, however, in the case of the dual of Baernstein's space, all those Szlenk derivations are…

Let $A$ be a separable amenable $C^*$-algebra and $B$ a non-unital and $\sigma$-unital simple $C^*$-algebra with continuous scale ($B$ need not be stable). We classify, up to unitary equivalence, all essential extensions of the form $0…

We introduce notions of compactness and weak compactness for multilinear maps from a product of normed spaces to a normed space, and prove some general results about these notions. We then consider linear maps $T:A\to B$ between Banach…

We prove that a large family of higher rank simple Lie groups (including $\rm SL_n (\mathbb{R})$ for $n \geq 3$) and their lattices have Banach property (T) with respect to all super-reflexive Banach spaces. Two consequences of this result…

We give examples of two Banach spaces. One Banach space has no spreading model which contains $\ell_p$ ($1\le p<\infty$) or $c_0$. The other space has an unconditional basis for which $\ell_p$ ($1\le p<\infty$) and $c_0$ are block finitely…

It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.