## Abstract and Applied Analysis

### Norm Attaining Arens Extensions on ${\ell }_{1}$

#### 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 ${\ell }_{1}$ 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

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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