Geodesic
Two characterizations of automorphisms on B(X)
Studia Mathematica, Tome 105 (1993) no. 2, pp. 143-149

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

DOI

Let X be an infinite-dimensional Banach space, and let ϕ be a surjective linear map on B(X) with ϕ(I) = I. If ϕ preserves injective operators in both directions then ϕ is an automorphism of the algebra B(X). If X is a Hilbert space, then ϕ is an automorphism of B(X) if and only if it preserves surjective operators in both directions. 
Peter Šemrl. Two characterizations of automorphisms on B(X). Studia Mathematica, Tome 105 (1993) no. 2, pp. 143-149. doi: 10.4064/sm-105-2-143-149
@article{10_4064_sm_105_2_143_149,
     author = {Peter \v{S}emrl},
     title = {Two characterizations of automorphisms on {B(X)}},
     journal = {Studia Mathematica},
     pages = {143--149},
     year = {1993},
     volume = {105},
     number = {2},
     doi = {10.4064/sm-105-2-143-149},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-105-2-143-149/}
}
TY  - JOUR
AU  - Peter Šemrl
TI  - Two characterizations of automorphisms on B(X)
JO  - Studia Mathematica
PY  - 1993
SP  - 143
EP  - 149
VL  - 105
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-105-2-143-149/
DO  - 10.4064/sm-105-2-143-149
LA  - en
ID  - 10_4064_sm_105_2_143_149
ER  - 
%0 Journal Article
%A Peter Šemrl
%T Two characterizations of automorphisms on B(X)
%J Studia Mathematica
%D 1993
%P 143-149
%V 105
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-105-2-143-149/
%R 10.4064/sm-105-2-143-149
%G en
%F 10_4064_sm_105_2_143_149

Cité par Sources :