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Norm attaining Arens extensions on \(\ell_1\). (English) Zbl 1449.46035

Summary: 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.

MSC:

46G25 (Spaces of) multilinear mappings, polynomials
46B04 Isometric theory of Banach spaces
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