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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the Arens product and annihilator algebras


Author: Pak-ken Wong
Journal: Proc. Amer. Math. Soc. 30 (1971), 79-83
MSC: Primary 46.50
DOI: https://doi.org/10.1090/S0002-9939-1971-0281005-2
MathSciNet review: 0281005
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Abstract: The purpose of this paper is to generalize two results in a recent paper by B. J. Tomiuk and the author. Let A be a ${B^ \ast }$-algebra and $M(A)$ the algebra of double centralizers of A. We show that A is a dual algebra if and only if $M(A)$ coincides with ${A^{ \ast \ast }}$. We also obtain that if A is an annihilator ${A^\ast }$-algebra, then ${\pi _A}(A)$ is a two-sided ideal of ${A^{ \ast \ast }}$.


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Keywords: Dual <!– MATH ${B^ \ast }$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${B^ \ast }$">-algebra, Arens product, double centralizer, annihilator algebra, minimal idempotent, group algebra of a compact group
Article copyright: © Copyright 1971 American Mathematical Society