Norm Attaining Multilinear Forms on ð ¿ 1 ( ð )

Yousef Saleh

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-6

Abstract:

Given an arbitrary measure 𠜇 , this study shows that the set of norm attaining multilinear forms is not dense in the space of all continuous multilinear forms on ð ¿ 1 ( 𠜇 ) . However, we have the density if and only if 𠜇 is purely atomic. Furthermore, the study presents an example of a Banach space ð ‘‹ in which the set of norm attaining operators from ð ‘‹ into ð ‘‹ ∗ is dense in the space of all bounded linear operators ð ¿ ( ð ‘‹ , ð ‘‹ ∗ ) . In contrast, the set of norm attaining bilinear forms on ð ‘‹ is not dense in the space of continuous bilinear forms on ð ‘‹ .

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:328481

DOI: 10.1155/2008/328481

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