Kadec-Klee properties of some quasi-Banach function spaces
type: Item
instance of: scholarly article
title: Kadec-Klee properties of some quasi-Banach function spaces
zbMATH Open document ID: 1411.46024
published in: Positivity
publication date: 2018-10-04T00:00:00Z
review text: A Banach space \(X\) is said to have the Kadec-Klee property if every sequence \((x_n)_{n\in \mathbb{N}}\) in \(X\) which is weakly convergent to some \(x\in X\) and satisfies \(\|x_n\|\to \|x\|\) is actually norm-convergent to \(x\). This paper concerns Kadec-Klee-type properties with respect to convergence in measure (instead of weak convergence) in quasi-Banach function spaces. Both global and local convergence in measure are considered. In particular, such properties are studied in symmetrizations of quasi-Banach function spaces, in Marcinkiewicz spaces and in Lorentz spaces.
reviewed by: Jan-David Hardtke
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 6946886
zbMATH Keywords: quasi-Banach function spaces
zbMATH Keywords: Kadec-Klee property
zbMATH Keywords: convergence in measure
zbMATH Keywords: Lorentz spaces
zbMATH Keywords: Marcinkiewicz spaces
author: Paweł Kolwicz
MaRDI profile type: Publication
full work available at URL: s11117-018-0555-8
OpenAlex ID: W2789084493
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DOI: 10.1007/S11117-018-0555-8
description: scientific article; zbMATH DE number 6946886