Bases in the spaces of homogeneous polynomials and multilinear operators on Banach spaces
| Autor: | Donghai Ji, Qingying Bu |
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| Rok vydání: | 2019 |
| Předmět: |
Sequence
Multilinear map Monomial homogeneous polynomials 46M05 Mathematics::Commutative Algebra Basis (linear algebra) General Mathematics Banach space Space (mathematics) Combinatorics monomial bases Homogeneous Bounded function symmetric tensor products 46B28 46G25 multilinear operators Mathematics |
| Zdroj: | Rocky Mountain J. Math. 49, no. 6 (2019), 1829-1842 |
| ISSN: | 0035-7596 |
| DOI: | 10.1216/rmj-2019-49-6-1829 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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