Abstract and Applied Analysis

Norm Attaining Arens Extensions on 1

Javier Falcó, Domingo García, Manuel Maestre, and Pilar Rueda

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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 1 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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 315641, 10 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412278779

Digital Object Identifier
doi:10.1155/2014/315641

Mathematical Reviews number (MathSciNet)
MR3198177

Zentralblatt MATH identifier
07022151

Citation

Falcó, Javier; García, Domingo; Maestre, Manuel; Rueda, Pilar. Norm Attaining Arens Extensions on ${\ell }_{1}$. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 315641, 10 pages. doi:10.1155/2014/315641. https://projecteuclid.org/euclid.aaa/1412278779


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