A theorem on isotropic spaces

Félix Cabello Sánchez

Studia Mathematica (1999)

  • Volume: 133, Issue: 3, page 257-260
  • ISSN: 0039-3223

Abstract

top
Let X be a normed space and G F ( X ) the group of all linear surjective isometries of X that are finite-dimensional perturbations of the identity. We prove that if G F ( X ) acts transitively on the unit sphere then X must be an inner product space.

How to cite

top

Cabello Sánchez, Félix. "A theorem on isotropic spaces." Studia Mathematica 133.3 (1999): 257-260. <http://eudml.org/doc/216617>.

@article{CabelloSánchez1999,
abstract = {Let X be a normed space and $G_F(X)$ the group of all linear surjective isometries of X that are finite-dimensional perturbations of the identity. We prove that if $G_F(X)$ acts transitively on the unit sphere then X must be an inner product space.},
author = {Cabello Sánchez, Félix},
journal = {Studia Mathematica},
keywords = {group of all linear surjective isometries; finite-dimensional perturbations of the identity; inner product space},
language = {eng},
number = {3},
pages = {257-260},
title = {A theorem on isotropic spaces},
url = {http://eudml.org/doc/216617},
volume = {133},
year = {1999},
}

TY - JOUR
AU - Cabello Sánchez, Félix
TI - A theorem on isotropic spaces
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 3
SP - 257
EP - 260
AB - Let X be a normed space and $G_F(X)$ the group of all linear surjective isometries of X that are finite-dimensional perturbations of the identity. We prove that if $G_F(X)$ acts transitively on the unit sphere then X must be an inner product space.
LA - eng
KW - group of all linear surjective isometries; finite-dimensional perturbations of the identity; inner product space
UR - http://eudml.org/doc/216617
ER -

References

top
  1. [1] H. Auerbach, Sur les groupes linéaires bornés I, Studia Math. 4 (1934), 113-127. Zbl59.1093.05
  2. [2] H. Auerbach, Sur une propriété caractéristique de l'ellipsoïde, ibid. 9 (1940), 17-22. Zbl0063.00135
  3. [3] S. Banach, Théorie des opérations linéaires, Monograf. Mat. 1, Warszawa-Lwów, 1932. Zbl0005.20901
  4. [4] F. Cabello Sánchez, Regards sur le problème des rotations de Mazur, Extracta Math. 12 (1997), 97-116. 
  5. [5] F. Cabello Sánchez, Maximal symmetric norms on Banach spaces, Proc. Roy. Irish Acad., to appear. 
  6. [6] P. Greim, J. E. Jamison and A. Kamińska, Almost transitivity of some function spaces, Math. Proc. Cambridge Philos. Soc. 116 (1994), 475-488. Zbl0835.46019
  7. [7] S. Mazur, Quelques propriétés caractéristiques des espaces euclidiens, C. R. Acad. Sci. Paris 207 (1938), 761-764. Zbl64.0376.03
  8. [8] S. Rolewicz, Metric Linear Spaces, Monograf. Mat. 56, PWN and D. Reidel, 1984. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.