Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 11, Number 1 (2017), 90-107.
Spaceability in norm-attaining sets
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 of the set , there exists a closed infinite-dimensional Banach subspace of the space of -linear forms on such that, for all nonzero elements of such a subspace, the Arens extension associated to the permutation of is norm-attaining if and only if is an element of . We also study the structure of the set of norm-attaining -linear forms on .
Banach J. Math. Anal., Volume 11, Number 1 (2017), 90-107.
Received: 18 November 2015
Accepted: 25 February 2016
First available in Project Euclid: 10 November 2016
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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