Geodesic
2-local Lie isomorphisms of operator algebras on Banach spaces
Lin Chen1 ; Lizhong Huang2 ; Fangyan Lu3
1 Department of Mathematics Soochow University Suzhou 215006, P.R. China and Department of Mathematics and Physics Anshun University Anshun 561000, P.R. China
2 Department of Mathematics Shanxi Datong University Datong 037009, P.R. China
3 Department of Mathematics Soochow University Suzhou 215006, P.R. China
Studia Mathematica, Tome 229 (2015) no. 1, pp. 1-11

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

Let $X$ and $Y$ be complex Banach spaces of dimension greater than 2. We show that every 2-local Lie isomorphism $\phi $ of $B(X)$ onto $B(Y)$ has the form $\phi =\varphi +\tau $, where $\varphi $ is an isomorphism or the negative of an anti-isomorphism of $B(X)$ onto $B(Y)$, and $\tau $ is a homogeneous map from $B(X)$ into $\mathbb CI$ vanishing on all finite sums of commutators.
DOI : 10.4064/sm7864-12-2015
Keywords: complex banach spaces dimension greater every local lie isomorphism phi has form phi varphi tau where varphi isomorphism negative anti isomorphism tau homogeneous map mathbb vanishing finite sums commutators

Lin Chen 1 ; Lizhong Huang 2 ; Fangyan Lu 3

1 Department of Mathematics Soochow University Suzhou 215006, P.R. China and Department of Mathematics and Physics Anshun University Anshun 561000, P.R. China
2 Department of Mathematics Shanxi Datong University Datong 037009, P.R. China
3 Department of Mathematics Soochow University Suzhou 215006, P.R. China 
@article{10_4064_sm7864_12_2015,
     author = {Lin Chen and Lizhong Huang and Fangyan Lu},
     title = {2-local {Lie} isomorphisms of operator algebras on {Banach} spaces},
     journal = {Studia Mathematica},
     pages = {1--11},
     publisher = {mathdoc},
     volume = {229},
     number = {1},
     year = {2015},
     doi = {10.4064/sm7864-12-2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm7864-12-2015/}
}
TY  - JOUR
AU  - Lin Chen
AU  - Lizhong Huang
AU  - Fangyan Lu
TI  - 2-local Lie isomorphisms of operator algebras on Banach spaces
JO  - Studia Mathematica
PY  - 2015
SP  - 1
EP  - 11
VL  - 229
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm7864-12-2015/
DO  - 10.4064/sm7864-12-2015
LA  - en
ID  - 10_4064_sm7864_12_2015
ER  - 
%0 Journal Article
%A Lin Chen
%A Lizhong Huang
%A Fangyan Lu
%T 2-local Lie isomorphisms of operator algebras on Banach spaces
%J Studia Mathematica
%D 2015
%P 1-11
%V 229
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm7864-12-2015/
%R 10.4064/sm7864-12-2015
%G en
%F 10_4064_sm7864_12_2015
Lin Chen; Lizhong Huang; Fangyan Lu. 2-local Lie isomorphisms of operator algebras on Banach spaces. Studia Mathematica, Tome 229 (2015) no. 1, pp. 1-11. doi: 10.4064/sm7864-12-2015

Cité par Sources :