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 .
"Spaceability in norm-attaining sets." Banach J. Math. Anal. 11 (1) 90 - 107, January 2017. https://doi.org/10.1215/17358787-3750182