Geodesic
Linear Maps on Factors which Preserve the Extreme Points of the Unit Ball
Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 434-441

Voir la notice de l'article provenant de la source Cambridge University Press

The aim of this paper is to characterize those linear maps from a von Neumann factor $A$ into itself which preserve the extreme points of the unit ball of $A$ . For example, we show that if $A$ is infinite, then every such linear preserver can be written as a fixed unitary operator times either a unital *-homomorphism or a unital $*$ -antihomomorphism.
DOI : 10.4153/CMB-1998-057-7
Mots-clés : 47B49, 47D25 
Mascioni, Vania; Molnár, Lajos. Linear Maps on Factors which Preserve the Extreme Points of the Unit Ball. Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 434-441. doi: 10.4153/CMB-1998-057-7
@article{10_4153_CMB_1998_057_7,
     author = {Mascioni, Vania and Moln\'ar, Lajos},
     title = {Linear {Maps} on {Factors} which {Preserve} the {Extreme} {Points} of the {Unit} {Ball}},
     journal = {Canadian mathematical bulletin},
     pages = {434--441},
     year = {1998},
     volume = {41},
     number = {4},
     doi = {10.4153/CMB-1998-057-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-057-7/}
}
TY  - JOUR
AU  - Mascioni, Vania
AU  - Molnár, Lajos
TI  - Linear Maps on Factors which Preserve the Extreme Points of the Unit Ball
JO  - Canadian mathematical bulletin
PY  - 1998
SP  - 434
EP  - 441
VL  - 41
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-057-7/
DO  - 10.4153/CMB-1998-057-7
ID  - 10_4153_CMB_1998_057_7
ER  - 
%0 Journal Article
%A Mascioni, Vania
%A Molnár, Lajos
%T Linear Maps on Factors which Preserve the Extreme Points of the Unit Ball
%J Canadian mathematical bulletin
%D 1998
%P 434-441
%V 41
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-057-7/
%R 10.4153/CMB-1998-057-7
%F 10_4153_CMB_1998_057_7

[BrSe] [BrSe] Brešar, M. and Šemrl, P., Linear preservers on B(X). Banach Cent. Publ. 38 (1997), 49–58. Google Scholar

[Hal] [Hal] Halmos, P. R., A Hilbert Space Problem Book. Van Nostrand, 1967. Google Scholar

[Her] [Her] Herstein, I. N., Jordan homomorphisms. Trans. Amer.Math. Soc. 81 (1956), 331–341. Google Scholar

[KaRi1] [KaRi1] Kadison, R. V. and Ringrose, J. R., Fundamentals of the Theory of Operator Algebras, Vol I. Academic Press, 1983. Google Scholar

[KaRi2] [KaRi2] Kadison, R. V. and Ringrose, J. R., Fundamentals of the Theory of Operator Algebras, Vol II. Academic Press, 1986. Google Scholar

[LaMa] [LaMa] Labuschagne, L. E. and Mascioni, V., Linear maps between C*-algebras whose adjoint preserve extreme points of the unit ball. Adv. in Math., to appear. Google Scholar

[LiTs] [LiTs] Li, C. K. and Tsing, N. K., Linear preserver problems: A brief introduction and some special techniques. Linear Algebra Appl. 162–164 (1992), 217–235. Google Scholar

[Mar] [Mar] Marcus, M., All linear operators leaving the unitary group invariant. Duke Math. J. 26 (1959), 155–163. Google Scholar

[Rai] [Rai] Rais, M., The unitary group preserving maps (the infinite dimensional case). Linear and Multilinear Algebra 20 (1987), 337–345. Google Scholar

[RuDy] [RuDy] Russo, B. and Dye, H. A., A note on unitary operators in C*-algebras. Duke Math. J. 33 (1966), 413–416. Google Scholar

[Sto] [Sto] Størmer, E., On the Jordan structure of C*-algebras. Trans. Amer.Math. Soc. 120 (1965), 438–447. Google Scholar

[StZs] [StZs] Strǎtilǎ, S. and Zsidó, L., Lectures on von Neumann Algebras. Abacus Press, 1979. Google Scholar

Cité par Sources :