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A CONVOLUTION-INDUCED TOPOLOGY ON THE ORLICZ SPACE OF A LOCALLY COMPACT GROUP
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 99 / Issue 1 / August 2015
- Published online by Cambridge University Press:
- 19 January 2015, pp. 1-11
- Print publication:
- August 2015
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- Article
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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.
