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Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces.

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Jiménez Sevilla, María del Mar and Payá Albert, Rafael (1998) Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces. Studia Mathematica, 127 (2). pp. 99-112. ISSN 0039-3223

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Official URL: https://eudml.org/doc/216467


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Abstract

For each natural number N, we give an example of a Banach space X such that the set of norm attaining N{linear forms is dense in the space of all continuous N{linear forms on X, but there are continuous (N +1){linear forms on X which cannot be approximated by norm attaining (N+1){linear forms. Actually, X is the canonical predual of a suitable Lorentz sequence space. We also get the analogous result for homogeneous polynomials.


Item Type:Article
Uncontrolled Keywords:Norm attaining multilinear forms and polynomials, weakly continuous multilinear forms and polynomials, Lorentz sequence spaces.
Subjects:Sciences > Mathematics > Algebra
ID Code:22372
Deposited On:12 Jul 2013 14:08
Last Modified:12 Dec 2018 15:08

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