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The Figa–Talamanca–Herz–Lebesgue Banach algebras $A_p^r(G)=A_p(G)\cap L^r(G)$

Published online by Cambridge University Press:  26 April 2006

EDMOND E. GRANIRER
EDMOND E. GRANIRER
Affiliation:
Department of Mathematics, The University of British Columbia, Vancouver BC, V2T 1Z2, Canada. e-mail: granirer@math.ubc.ca
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Abstract

Functional analytic properties of the Banach Algebras $A_p^r(G)$ such as Arens regularity, amenability, weak sequential completeness, sets of synthesis and strict containment for fixed $p$ and increasing $r$, are investigated.

It is found that $A_p^r(G)$, $1\leq r<\infty$, behave very differently to the Figa–Talamanca–Herz algebras $A_p(G)$.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 140 , Issue 3 , May 2006 , pp. 401 - 416
Copyright
2006 Cambridge Philosophical Society

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