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A CONVOLUTION-INDUCED TOPOLOGY ON THE ORLICZ SPACE OF A LOCALLY COMPACT GROUP

Part of: Abstract harmonic analysis Linear function spaces and their duals Topological linear spaces and related structures

Published online by Cambridge University Press:  19 January 2015

IBRAHIM AKBARBAGLU  and
SAEID MAGHSOUDI
IBRAHIM AKBARBAGLU
Affiliation:
Department of Mathematics, Faculty of Basic Sciences, University of Bonab, Bonab 55517-61167, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran email ibrahim.akbarbaglu@gmail.com
SAEID MAGHSOUDI*
Affiliation:
Department of Mathematics, University of Zanjan, Zanjan 45195-313, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran email s_maghsodi@znu.ac.ir
*
✉s_maghsodi@znu.ac.ir
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Abstract

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Let $G$ be a locally compact group with a fixed left Haar measure. In this paper, given a strictly positive Young function ${\rm\Phi}$, we consider $L^{{\rm\Phi}}(G)$ as a Banach left $L^{1}(G)$-module. Then we equip $L^{{\rm\Phi}}(G)$ with the strict topology induced by $L^{1}(G)$ in the sense of Sentilles and Taylor. Some properties of this locally convex topology and a comparison with weak$^{\ast }$, bounded weak$^{\ast }$ and norm topologies are presented.

Keywords

Orlicz spacelocally compact groupconvolutionstrict topologybounded weak∗ topology

MSC classification

Primary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Secondary: 46A70: Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 46A03: General theory of locally convex spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 1 , August 2015 , pp. 1 - 11
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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