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Search: MSC category 58B99 ( None of the above, but in this section )

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1. CMB 2002 (vol 45 pp. 3)

Azagra, D.; Dobrowolski, T.
 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 \setminus \{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 \setminus 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. Categories:46B20, 58B99

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