Related papers: Weakly countably determined spaces of high complex…

We show that the Rochberg spaces induced by complex interpolation form themselves complex interpolation scales, obtain the interpolated spaces and associated derivations. We present our results in the context of analytic families of Banach…

We propose a new class of hypertopologies, called here weak$^{\ast }$ hypertopologies, on the dual space $\mathcal{X}^{\ast }$ of a real or complex topological vector space $\mathcal{X}$. The most well-studied and well-known hypertopology…

In this paper we show that if $(y_n)$ is a seminormalized sequence in a Banach space which does not have any weakly convergent subsequence, then it contains a wide-$(s)$ subsequence $(x_n)$ which admits an equivalent convex basic sequence.…

We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that…

The question is addressed of when a Sobolev type space, built upon a general rearrangement-invariant norm, on an $n$-dimensional domain, is a Banach algebra under pointwise multiplication of functions. A sharp balance condition among the…

We describe a class of sharply o-minimal structures, called analytically generated structures, whose definable sets and their complexity filtration are determined by the collection of definable complex cells. We prove a polynomially…

There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern exposition of the subtle differences between key results and…

Coorbit theory is a powerful machinery that constructs a family of Banach spaces, the so-called coorbit spaces, from well-behaved unitary representations of locally compact groups. A core feature of coorbit spaces is that they can be…

This paper deals with the interplay of the geometry of the norm and the weak topology in Banach spaces. Both dual and intrinsic connections between weak forms of rotundity and smoothness ared discussed. Weakly exposed points, weakly locally…

We give a new proof of the "weakly admissible implies admissible" theorem of Colmez and Fontaine describing the semi-stable p-adic representations. We study Banach-Colmez spaces, i.e. p-adic Banach spaces with the extra data of a…

Through careful analysis of types inspired by [AGTW21] we characterize a notion of definable compactness for definable topologies in general o-minimal structures, generalizing results from [PP07] about closed and bounded definable sets in…

Answering a question raised by V. V. Tkachuk, we present several examples of $\sigma$-compact spaces, some only consistent and some in ZFC, that are not countably tight but in which the closure of any discrete subset is countably tight. In…

We study two form of selective selective separability, $SS$ and $SS^+$, on countable spaces with an analytic topology. We show several Ramsey type properties which imply $SS$. For analytic spaces $X$, $SS^+$ is equivalent to have that the…

Let $X$ be a Banach space and $\mu$ a probability measure. A set $K \subseteq L^1(\mu,X)$ is said to be a $\delta\mathcal{S}$-set if it is uniformly integrable and for every $\delta>0$ there is a weakly compact set $W \subseteq X$ such that…

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly…

We introduce a class of analytic sheaves in a Banach space X, that we call cohesive sheaves. Cohesion is meant to generalize the notion of coherence from finite dimensional analysis. Accordingly, we prove the analog of Cartan's Theorems A…

A theorem of Davis, Figiel, Johnson and Pe{\l}czy\'nski tells us that weakly-compact operators between Banach spaces factor through reflexive Banach spaces. The machinery underlying this result is that of the real interpolation method,…

In this paper, we study nonlinear embeddings between Banach spaces. More specifically, the goal of this paper is to study weaker versions of coarse and uniform embeddability, and to provide suggestive evidences that those weaker embeddings…

We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from…

We construct a countable inductive limit of weighted Banach spaces of holomorphic functions, which is not a topological subspace of the corresponding weighted inductive limit of spaces of continuous functions. The main step of our…