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MORE ON THE ARENS REGULARITY OF $B(X)$

Part of: Topological algebras, normed rings and algebras, Banach algebras Linear spaces and algebras of operators

Published online by Cambridge University Press:  01 March 2016

R. FAAL  and
H. R. EBRAHIMI VISHKI
R. FAAL
Affiliation:
Department of Pure Mathematics, Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran email faal.ramin@yahoo.com
H. R. EBRAHIMI VISHKI*
Affiliation:
Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran email vishki@um.ac.ir
*
✉vishki@um.ac.ir
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Abstract

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We focus on a question raised by Daws [‘Arens regularity of the algebra of operators on a Banach space’, Bull. Lond. Math. Soc.36 (2004), 493–503] concerning the Arens regularity of $B(X)$, the algebra of operators on a Banach space $X$. Among other things, we show that $B(X)$ is Arens regular if and only if $X$ is ultrareflexive.

Keywords

Arens productsalgebra of operatorsreflexive spacesuperreflexiveweak operator topologyultrapower

MSC classification

Primary: 47L10: Algebras of operators on Banach spaces and other topological linear spaces
Secondary: 46H25: Normed modules and Banach modules, topological modules (if not placed in or ) 47L50: Dual spaces of operator algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 2 , October 2016 , pp. 296 - 303
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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