Norm attainment for multilinear operators and polynomials on Banach Spaces and Banach lattices
Year: 2026
Type: preprint
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 $X_1, \dots, X_n$ and $Y$ ensuring that every $A \in \mathcal{L}(X_1, \dots, X_n; Y)$ (respectively, $P \in \mathcal{P}(^n X_1; Y)$) 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.
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160987298