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The Second Conjugates of Certain Banach Algebras

Published online by Cambridge University Press:  20 November 2018

Pak-Ken Wong
Pak-Ken Wong*
Affiliation:
Seton Hall University, South Orange, New Jersey
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Let A be a Banach algebra and A** its second conjugate space. Arens has denned two natural extensions of the product on A to A**. Under either Arens product, A** becomes a Banach algebra. Let A be a semisimple Banach algebra which is a dense two-sided ideal of a B*-algebra B and R** the radical of (A**, o). We show that A** = Q ⊕ R**, where Q is a closed two-sided ideal of A**, o). This was inspired by Alexander's recent result for simple dual A*-algebras (see [1, p. 573, Theorem 5]). We also obtain that if A is commutative, then A is Arens regular.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1029 - 1035
Copyright
Copyright © Canadian Mathematical Society 1975

References

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