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WEIGHTED ORLICZ ALGEBRAS ON LOCALLY COMPACT GROUPS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 99 / Issue 3 / December 2015
- Published online by Cambridge University Press:
- 02 September 2015, pp. 399-414
- Print publication:
- December 2015
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- Article
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- You have access
- Export citation
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For a locally compact group
$G$ with left Haar measure and a Young function 
${\rm\Phi}$, we define and study the weighted Orlicz algebra 
$L_{w}^{{\rm\Phi}}(G)$ with respect to convolution. We show that 
$L_{w}^{{\rm\Phi}}(G)$ admits no bounded approximate identity under certain conditions. We prove that a closed linear subspace 
$I$ of the algebra 
$L_{w}^{{\rm\Phi}}(G)$ is an ideal in 
$L_{w}^{{\rm\Phi}}(G)$ if and only if 
$I$ is left translation invariant. For an abelian 
$G$, we describe the spectrum (maximal ideal space) of the weighted Orlicz algebra and show that weighted Orlicz algebras are semisimple.
