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.


46G25 (Spaces of) multilinear mappings, polynomials
46B04 Isometric theory of Banach spaces
Full Text: DOI


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