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AN ARBITRARY INTERSECTION OF Lp-SPACES

Published online by Cambridge University Press:  16 February 2012

F. ABTAHI*
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran (email: f.abtahi@sci.ui.ac.ir)
H. G. AMINI
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran (email: ghaeidamini@mau.ac.ir)
H. A. LOTFI
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran (email: hali-lotfi@yahoo.com)
A. REJALI
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran (email: rejali@sci.ui.ac.ir)
*
For correspondence; e-mail: abtahi.fatemeh@gmail.com
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Abstract

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For a locally compact group G and an arbitrary subset J of [1,], we introduce ILJ(G) as a subspace of ⋂ pJLp(G) with some norm to make it a Banach space. Then, for some special choice of J, we investigate some topological and algebraic properties of ILJ(G) as a Banach algebra under a convolution product.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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