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Abstract and Applied Analysis
Volume 2014, Article ID 315641, 10 pages
http://dx.doi.org/10.1155/2014/315641
Research Article

Norm Attaining Arens Extensions on

1Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
2Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, Burjasot, 46100 Valencia, Spain

Received 23 December 2013; Accepted 6 February 2014; Published 8 April 2014

Academic Editor: Miguel Martín

Copyright © 2014 Javier Falcó et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study norm attaining properties of the Arens extensions of multilinear forms defined on Banach spaces. Among other related results, we construct a multilinear form on with the property that only some fixed Arens extensions determined a priori attain their norms. We also study when multilinear forms can be approximated by ones with the property that only some of their Arens extensions attain their norms.