PreprintarXiv licencearXiv
Norm attainment for multilinear operators and polynomials on Banach Spaces and Banach lattices
Abstract
We study norm attainment for multilinear operators and homogeneous polynomials between Banach spaces, as well as for positive multilinear operators between Banach lattices. We establish multilinear and polynomial versions of [23, Theorem B] and [35, Theorem 2.12]. More precisely, we provide sufficient conditions on Banach spaces X1, …, Xn and Y ensuring that every A ∈ ℒ(X1, …, Xn; Y) (respectively, P ∈ 𝒫(n X1; Y)) is weakly sequentially continuous if and only if it attains its norm. We also obtain analogous results for positive n-linear operators and positive n-homogeneous polynomials in the setting of Banach lattices.
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BibTeX
@misc{garcia2026norm,
title = {{Norm attainment for multilinear operators and polynomials on Banach Spaces and Banach lattices}},
author = {Luis A. Garcia and José Lucas P. Luiz and Vinícius C. C. Miranda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.12117},
eprint = {2605.12117},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.12117},
}
RIS
TY - UNPB
TI - Norm attainment for multilinear operators and polynomials on Banach Spaces and Banach lattices
AU - Luis A. Garcia
AU - José Lucas P. Luiz
AU - Vinícius C. C. Miranda
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2605.12117
UR - https://arxiv.org/abs/2605.12117
AB - We study norm attainment for multilinear operators and homogeneous polynomials between Banach spaces, as well as for positive multilinear operators between Banach lattices. We establish multilinear and polynomial versions of [23, Theorem B] and [35, Theorem 2.12]. More precisely, we provide sufficient conditions on Banach spaces X_1, …, X_n and Y ensuring that every A ∈ ℒ(X_1, …, X_n; Y) (respectively, P ∈ 𝒫(^n X_1; Y)) is weakly sequentially continuous if and only if it attains its norm. We also obtain analogous results for positive n-linear operators and positive n-homogeneous polynomials in the setting of Banach lattices.
ER -