Uniformly \(\mu \)-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 0970.46015
author: Krzysztof Feledziak
publication date: 2001-06-10T00:00:00Z
full work available at URL: https://eudml.org/doc/22354
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46A70
zbMATH DE Number: 1602719
zbMATH Keywords: Köthe-Bochner spaces
zbMATH Keywords: Orlicz-Bochner spaces
zbMATH Keywords: locally solid topology
zbMATH Keywords: generalized mixed topology
zbMATH Keywords: inductive limit topology
zbMATH Keywords: uniformly \(\mu \)-continuous topology
MaRDI profile type: Publication
title: Uniformly \(\mu \)-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces
published in: Commentationes Mathematicae Universitatis Carolinae
review text: The author gives an account of locally solid topologies and studies mutual relations of uniformly \(\mu \)-continuous topologies, uniformly \(\mu \)-continuous solid pseudonorms, and uniformly summable pseudonorms. In Köthe-Bochner spaces he proves a characterization of uniformly \(\mu \)-continuous locally solid topologies in terms of uniformly summable pseudonorms. NEWLINENEWLINENEWLINEFurther, he shows that the finest uniformly \(\mu \)-continuous topology on an Orlicz-Bochner space is the generalized mixed topology, which coincides here with the concept of a strictly inductive limit of balanced topological spaces. In this frame a characterization of \(\gamma _{\varphi }\)-linear mappings is given.
reviewed by: Miroslav Krbec
description: scientific article