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ARENS REGULARITY OF MODULE ACTIONS AND THE SECOND ADJOINT OF A DERIVATION

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  01 June 2008

S. MOHAMMADZADEH  and
H. R. E. VISHKI
S. MOHAMMADZADEH
Affiliation:
Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran (email: [email protected])
H. R. E. VISHKI*
Affiliation:
Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran Centre of Excellence in Analysis on Algebraic Strutures (CEAAS), Ferdowski University of Mashhad, Mashhad, Iran (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper, we give a simple criterion for the Arens regularity of a bilinear mapping on normed spaces, which applies in particular to Banach module actions, and then investigate those conditions under which the second adjoint of a derivation into a dual Banach module is again a derivation. As a consequence of the main result, a simple and direct proof for several older results is also included.

Keywords

Arens productbounded bilinear mapBanach module actionderivationmodule actionsecond dual

MSC classification

Secondary: 46H20: Structure, classification of topological algebras 46H25: Normed modules and Banach modules, topological modules (if not placed in or )
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 3 , June 2008 , pp. 465 - 476
Copyright
Copyright © 2008 Australian Mathematical Society

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