Banach Journal of Mathematical Analysis

Spaceability in norm-attaining sets

Javier Falcó, Domingo García, Manuel Maestre, and Pilar Rueda

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Abstract

We study the existence of infinite-dimensional vector spaces in the sets of norm-attaining operators, multilinear forms, and polynomials. Our main result is that, for every set of permutations P of the set {1,,n}, there exists a closed infinite-dimensional Banach subspace of the space of n-linear forms on 1 such that, for all nonzero elements B of such a subspace, the Arens extension associated to the permutation σ of B is norm-attaining if and only if σ is an element of P. We also study the structure of the set of norm-attaining n-linear forms on c0.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 1 (2017), 90-107.

Dates
Received: 18 November 2015
Accepted: 25 February 2016
First available in Project Euclid: 10 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1478746988

Digital Object Identifier
doi:10.1215/17358787-3750182

Mathematical Reviews number (MathSciNet)
MR3571146

Zentralblatt MATH identifier
1366.46032

Subjects
Primary: 46G25: (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]
Secondary: 46B20: Geometry and structure of normed linear spaces

Keywords
norm-attaining multilinear mapping Arens extension Banach space

Citation

Falcó, Javier; García, Domingo; Maestre, Manuel; Rueda, Pilar. Spaceability in norm-attaining sets. Banach J. Math. Anal. 11 (2017), no. 1, 90--107. doi:10.1215/17358787-3750182. https://projecteuclid.org/euclid.bjma/1478746988


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