Multipliers on complemented Banach algebras

Author:
Bohdan J. Tomiuk

Journal:
Proc. Amer. Math. Soc. **115** (1992), 397-404

MSC:
Primary 46H10

MathSciNet review:
1116273

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Abstract: Let be a semisimple right complemented Banach algebra, the left regular representation of , and the left multiplier algebra of . In this paper we are concerned with and its relationship to and . We show that is an annihilator algebra and that it is a closed ideal of . Moreover, and have the same socle. We also show that the left multiplier algebra of a minimal closed ideal of is topologically algebra isomorphic to , the algebra of bounded linear operators on a Hilbert space . Conditions are given under which is right complemented.

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DOI:
https://doi.org/10.1090/S0002-9939-1992-1116273-1

Keywords:
Right complemented Banach algebra,
dual Banach algebra,
left regular representation,
left multiplier,
abstract Segal algebra

Article copyright:
© Copyright 1992
American Mathematical Society