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AN ARBITRARY INTERSECTION OF Lp-SPACES

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  16 February 2012

F. ABTAHI ,
H. G. AMINI ,
H. A. LOTFI  and
A. REJALI
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 ⋂ p∈JLp(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.

Keywords

amenabilityapproximate amenabilityapproximate identityidealmultiplierLp-spaceweak amenability

MSC classification

Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups 43A20: $L^1$-algebras on groups, semigroups, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 3 , June 2012 , pp. 433 - 445
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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