The multipliers related products in Banach algebras

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.

Mathematics Subject Classification (2010):

• 43A07
• 43A22
• 46H25

Keywords:

• Multiplier
• Arens regular
• Banach modules
• approximately amenable
• Banach algebras