The multiplier algebra and BSE property of the direct sum of Banach algebras

Authors

  • Z. Kamali
  • M. Lashkarizadeh Bami

Keywords:

Commutative Banach algebra, Multiplier algebra, BSE algebra, Direct sum

Abstract

The notion of BSE-algebras were introduced and first sudied by Takahasi and Hatori and later by Kaniuth and U¨ lger. This notation depends strongly on multiplier algebra M(A) of the commutative Banach algebra A. In this paper we first present a characterization of the multiplier algebra of direct sum of two commutative semisimple Banach algebras. Then as an application we show that A B is a BSE algebra if and only if A and B are BSE. We also prove that if the algebra A B with 􀀀Lau product is a BSE algebra and B is unital then B is a BSE algebra. We present some examples which show that BSE property of A B does not imply BSE property of A, even in the case when B is unital. 10.1017/S0004972712001001

Published

2013-08-11

Issue

Vol. 88 No. 2 (2013)

Section

Articles
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