Year: 2026
Type: preprint
Abstract: We study the spaces of bounded multilinear operators $\mathcal L^i(X,Y)$ endowed with $L^p_μ$-norms, where $X,Y$ are normed spaces and $μ$ is a measure with $p$-moments. These are norms without taking a quotient, under suitable support conditions. The topology induced coincides with the strong operator and compact-open topologies on operator-norm-bounded subsets. Furthermore, we identify the completion of these spaces with spaces of Hilbert--Schmidt operators on the reproducing kernel Hilbert space (RKHS) for $p=2$; with iterated $γ$-radonifying multilinear operators on the RKHS in the Gaussian case, for general $p$.
Source: arXiv (Cornell University)
Author: de Feo, Filippo
Institution: Technische Universität Berlin
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Awards: G5709080070, G7650316851
OpenAlex ID: W7222291352