Original Articles

The multipliers related products in Banach algebras

Published in: Quaestiones Mathematicae
Volume 37 , issue 4 , 2014 , pages: 507–523

DOI: 10.2989/16073606.2013.779988

Author(s): Javad Laali Department of Mathematical Sciences and Computer, Iran

Keywords: 43A07 , 43A22 , 46H25 , 43A07 , 43A22 , 46H25

Abstract

For a Banach algebra and a bounded multiplier T of , there is a new Banach algebra _T, related to and T, that has the same underlying space as . We investigate the relationship between the Banach algebras and _T. It is shown that is Arens regular (resp. approximately amenable, approximately weakly amenable) if and only if _T is, under certain conditions. We show that, for the group algebra L¹(G) of a locally compact group G, there exists a multiplier T such that L¹(G)_T is Arens regular if and only if G is compact, so that, L¹(G) and L¹(G)_T do not have the same properties.

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