Arens Regularity of Module Actions and the Second Adjoit of a Derivation

2007/11/10 by Somayeh Mohammadzadeh, S. Mohammadzadeh, Mohammadzadeh, S. +3
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Functional Equations Stability Results #math.FA #msc:46H20 #msc:46H25

paper · pdf · doi:10.48550/arxiv.0711.1621

15 pages. To appear in Bull. Austral. Math. Soc

arxiv created 2007/11/10 · arxiv updated 2009/12/01

Abstract

In this paper, first 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 we 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.

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