Special symmetries of Banach spaces isomorphic to Hilbert spaces

Jarno Talponen. "Special symmetries of Banach spaces isomorphic to Hilbert spaces." Studia Mathematica 200.1 (2010): 31-40. <http://eudml.org/doc/285888>.

@article{JarnoTalponen2010,
abstract = {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.},
author = {Jarno Talponen},
journal = {Studia Mathematica},
keywords = {Hilbert spaces; group of isometries},
language = {eng},
number = {1},
pages = {31-40},
title = {Special symmetries of Banach spaces isomorphic to Hilbert spaces},
url = {http://eudml.org/doc/285888},
volume = {200},
year = {2010},
}

TY - JOUR
AU - Jarno Talponen
TI - Special symmetries of Banach spaces isomorphic to Hilbert spaces
JO - Studia Mathematica
PY - 2010
VL - 200
IS - 1
SP - 31
EP - 40
AB - 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.
LA - eng
KW - Hilbert spaces; group of isometries
UR - http://eudml.org/doc/285888
ER -