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2019 Bases in the spaces of homogeneous polynomials and multilinear operators on Banach spaces
Donghai Ji, Qingying Bu
Rocky Mountain J. Math. 49(6): 1829-1842 (2019). DOI: 10.1216/RMJ-2019-49-6-1829

Abstract

For Banach spaces $E_1, \dots ,E_m$, $E$ and $F$ with their bases, we show that a particular monomial sequence forms a basis of $\mathcal {P}(^mE; F)$, the space of continuous $m$-homogeneous polynomials from $E$ to $F$ (resp.\ a basis of $\mathcal {L}(E_1,\dots ,E_m;F)$, the space of continuous $m$-linear operators from $E_1\times \cdots \times E_m$ to $F$) if and only if the basis of $E$ (resp. the basis of $E_1,\dots ,E_m$) is a shrinking basis and every $P \in \mathcal {P}(^mE; F)$ (resp.\ every $T \in \mathcal {L}(E_1,\dots ,E_m;F)$) is weakly continuous on bounded sets.

Citation

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Donghai Ji. Qingying Bu. "Bases in the spaces of homogeneous polynomials and multilinear operators on Banach spaces." Rocky Mountain J. Math. 49 (6) 1829 - 1842, 2019. https://doi.org/10.1216/RMJ-2019-49-6-1829

Information

Published: 2019
First available in Project Euclid: 3 November 2019

zbMATH: 07136580
MathSciNet: MR4027235
Digital Object Identifier: 10.1216/RMJ-2019-49-6-1829

Subjects:
Primary: 46G25
Secondary: 46B28, 46M05

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 6 • 2019
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