PreprintCC0arXiv
Lpμ-Normed Spaces of Bounded Multilinear Operator
Abstract
We study the spaces of bounded multilinear operators ℒi(X,Y) endowed with Lpμ-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.
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BibTeX
@misc{feo2026lpμnormed,
title = {{$L^p_μ$-Normed Spaces of Bounded Multilinear Operator}},
author = {Filippo de Feo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19151},
eprint = {2610.19151},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19151},
note = {CC0},
}
RIS
TY - UNPB
TI - L^p_μ-Normed Spaces of Bounded Multilinear Operator
AU - Filippo de Feo
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.19151
UR - https://arxiv.org/abs/2610.19151
AB - We study the spaces of bounded multilinear operators 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.
ER -