Approximately multiplicative maps between algebras of bounded operators on Banach spaces
| Autor: | Yemon Choi, Bence Horváth, Niels Jakob Laustsen |
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| Rok vydání: | 2021 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2110.04072 |
| Popis: | We show that for any separable reflexive Banach space $X$ and a large class of Banach spaces $E$, including those with a subsymmetric shrinking basis but also all spaces $L_p$ for $1\leq p \leq \infty$, every bounded linear map ${\mathcal B}(E)\to {\mathcal B}(X)$ which is approximately multiplicative is necessarily close in the operator norm to some bounded homomorphism ${\mathcal B}(E)\to {\mathcal B}(X)$. That is, the pair $({\mathcal B}(E), {\mathcal B}(X))$ has the AMNM property in the sense of Johnson (\textit{J.~London Math.\ Soc.} 1988). Previously this was only known for $E=X=\ell_p$ with $1 Comment: v1: AMS-LaTeX, 30 pages. Submitted for publication. v2: incorporates revisions based on feedback from referee; minor updates/corrections to bibliography. Final accepted version, to appear in Trans. Amer. Math. Soc |
| Databáze: | OpenAIRE |
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