Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications
We prove that every infinite-dimensional Banach space X having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to X \ {0}. More generally, if X is an infinite-dimensional Banach space and F is a closed subspace of X such that there is a real-analytic seminorm on X wh...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2002 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/57114 |
| Online Access: | https://hdl.handle.net/20.500.14352/57114 |
| Access Level: | Open access |
| Keyword: | 517.98 Real-analytic diffeomorphic Real-analytic seminorm Análisis funcional y teoría de operadores |
| Summary: | We prove that every infinite-dimensional Banach space X having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to X \ {0}. More generally, if X is an infinite-dimensional Banach space and F is a closed subspace of X such that there is a real-analytic seminorm on X whose set of zeros is F, and X / F is infinite-dimensional, then X and X \ F are real-analytic diffeomorphic. As an application we show the existence of real-analytic free actions of the circle and the n-torus on certain Banach spaces |
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