Open Access
January 2017 Spaceability in norm-attaining sets
Javier Falcó, Domingo García, Manuel Maestre, Pilar Rueda
Banach J. Math. Anal. 11(1): 90-107 (January 2017). DOI: 10.1215/17358787-3750182


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.


Download Citation

Javier Falcó. Domingo García. Manuel Maestre. Pilar Rueda. "Spaceability in norm-attaining sets." Banach J. Math. Anal. 11 (1) 90 - 107, January 2017.


Received: 18 November 2015; Accepted: 25 February 2016; Published: January 2017
First available in Project Euclid: 10 November 2016

zbMATH: 1366.46032
MathSciNet: MR3571146
Digital Object Identifier: 10.1215/17358787-3750182

Primary: 46G25
Secondary: 46B20

Keywords: Arens extension , Banach space , multilinear mapping , norm-attaining

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 1 • January 2017
Back to Top