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A strict topology on Orlicz spaces
Author(s) -
Akbarbaglu I.,
Maghsoudi S.,
SeoaneSepúlveda J. B.
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400100
Subject(s) - mathematics , radon measure , topology (electrical circuits) , locally compact space , weak topology (polar topology) , general topology , convolution (computer science) , space (punctuation) , topological group , function space , locally convex topological vector space , function (biology) , measure (data warehouse) , compact open topology , haar measure , topological space , extension topology , pure mathematics , interpolation space , functional analysis , combinatorics , computer science , database , chemistry , biology , operating system , biochemistry , machine learning , evolutionary biology , artificial neural network , gene
Let φ be a Young function, Ω be a locally compact space, and μ be a positive Radon measure on Ω. We consider a strict topology β φ (in the sense of Sentilles‐Taylor) on the Orlicz function spaceM φ ( Ω )and investigate various properties of this locally convex topology. We also study the Orlicz spaceM φ ( G )of a locally compact group G with a left Haar measure under the strict topology β φ and certain other natural locally convex topologies. Finally we present some results on various continuity properties of convolution operators onM φ ( G )under the β φ topology and other natural ones.