Special symmetries of Banach spaces isomorphic to Hilbert spaces

• Autorzy: Jarno Talponen
• Języki publikacji: EN

Abstrakty

EN

We characterize Hilbert spaces among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical: 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.

Kategorie tematyczne

• 43A07: Means on groups, semigroups, etc.; amenable groups
• 46B08: Ultraproduct techniques in Banach space theory
• 43A35: Positive definite functions on groups, semigroups, etc.
• 46C15: Characterizations of Hilbert spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 200
• Numer: 1
• Strony: 31-40

Daty

wydano

2010

Twórcy

autor

Jarno Talponen

• Institute of Mathematics, Aalto University, P.O. Box 1100, FI-00076 Aalto, Finland

Identyfikatory

DOI

10.4064/sm200-1-2