This is an announcement for the paper "Special symmetries of Banach spaces isomorphic to Hilbert spaces" by Jarno Talponen.

Abstract: In this paper Hilbert spaces are characterized among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical here: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space.

Archive classification: math.FA

Mathematics Subject Classification: 46C15; 46B04

The source file(s), SSNSb.tex: 30955 bytes, is(are) stored in gzipped form as 0809.1789.gz with size 9kb. The corresponding postcript file has gzipped size 74kb.

Submitted from: talponen@cc.helsinki.fi

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http://front.math.ucdavis.edu/0809.1789

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http://arXiv.org/abs/0809.1789

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