Nonlinear aspects of super weakly compact sets

关于弱紧集为超弱紧集的空间的弱序列完备性

On weak sequential completeness of spaces where weakly compact sets are super weakly compact

本文证明弱紧集为超弱紧集的 Banach 空间自动弱序列完备，回答了 Silber (2024) 的问题，并利用求和子列从非平凡弱 Cauchy 列构造非超弱紧的弱紧集。

Metrical Characterizations of super weakly compact operators

We characterize super weakly compact operators as those through which binary tree and diamond and Laakso graphs may not be factored with uniform distortion.

On the cohomology of weakly almost periodic group representations

We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a vanishing result for the restriction map (with respect to a subgroup) in the reduced cohomology of weakly periodic representations. Combined with the Alaoglu-Birkhoff decomposition theorem, this generalizes and complements theorems on continuous group cohomology by several authors.

Lipschitz-free spaces over compact subsets of superreflexive spaces are weakly sequentially complete

Let $M$ be a compact subset of a superreflexive Banach space. We prove that the Lipschitz-free space $\mathcal{F}(M)$, the predual of the Banach space of Lipschitz functions on $M$, has the Pełczyński's property ($V^\ast$). As a consequence, the Lipschitz-free space $\mathcal{F}(M)$ is weakly sequentially complete.

Denseness of Sets of Supercyclic Vectors

The sets of strongly supercyclic, weakly l-sequentially supercyclic, weakly sequentially supercyclic, and weakly supercyclic vectors for an arbitrary normed-space operator are all dense in the normed space, regardless the notion of denseness one is considering, provided they are nonempty.

Boundedly Spaced Subsequences and Weak Dynamics

The purpose of this paper is to characterize weak supercyclicity for Hilbert-space contractions, which is shown to be equivalent to characterizing weak supercyclicity for unitary operators$.$ This is naturally motivated by an open question that asks whether every weakly supercyclic power bounded operator is weakly stable (which in turn is naturally motivated by a result that asserts that every supercyclic power bounded operator is strongly stable)$.$ Precisely, weakly supercyclicity is investigated in light of boundedly spaced subsequences as discussed in Lemma 3.1$.$ The main result in Theore…