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...

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Bibliographic Details
Authors: Azagra Rueda, Daniel, Dobrowolski, Tadeusz
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
Description
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