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A CONVOLUTION-INDUCED TOPOLOGY ON THE ORLICZ SPACE OF A LOCALLY COMPACT GROUP
Published online by Cambridge University Press: 19 January 2015
Abstract
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.
- Type
- Research Article
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- © 2015 Australian Mathematical Publishing Association Inc.