On the Arens product and commutative Banach algebras

Author:
Pak Ken Wong

Journal:
Proc. Amer. Math. Soc. **37** (1973), 111-113

MSC:
Primary 46H99; Secondary 46J05

DOI:
https://doi.org/10.1090/S0002-9939-1973-0306912-5

MathSciNet review:
0306912

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Abstract: The purpose of this note is to generalize two recent results by the author for commutative Banach algebras. Let *A* be a commutative Banach algebra with carrier space and the canonical embedding of *A* into its second conjugate space (with the Arens product). We show that if *A* is a semisimple annihilator algebra, then is a two-sided ideal of . We also obtain that if *A* is a dense two-sided ideal of , then is a two-sided ideal of if and only if *A* is a modular annihilator algebra.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0306912-5

Keywords:
Arens product,
modular annihilator,
annihilator algebra,
carrier space

Article copyright:
© Copyright 1973
American Mathematical Society