Linear maps preserving quasi-commutativity

Heydar Radjavi, and Peter Šemrl. "Linear maps preserving quasi-commutativity." Studia Mathematica 184.2 (2008): 191-204. <http://eudml.org/doc/284559>.

@article{HeydarRadjavi2008,
abstract = {Let X and Y be Banach spaces and ℬ(X) and ℬ(Y) the algebras of all bounded linear operators on X and Y, respectively. We say that A,B ∈ ℬ(X) quasi-commute if there exists a nonzero scalar ω such that AB = ωBA. We characterize bijective linear maps ϕ : ℬ(X) → ℬ(Y) preserving quasi-commutativity. In fact, such a characterization can be proved for much more general algebras. In the finite-dimensional case the same result can be obtained without the bijectivity assumption.},
author = {Heydar Radjavi, Peter Šemrl},
journal = {Studia Mathematica},
keywords = {linear preserver; quasi-commutativity; commutant; quasi-commutant; Banach spaces; bounded linear operators},
language = {eng},
number = {2},
pages = {191-204},
title = {Linear maps preserving quasi-commutativity},
url = {http://eudml.org/doc/284559},
volume = {184},
year = {2008},
}

TY - JOUR
AU - Heydar Radjavi
AU - Peter Šemrl
TI - Linear maps preserving quasi-commutativity
JO - Studia Mathematica
PY - 2008
VL - 184
IS - 2
SP - 191
EP - 204
AB - Let X and Y be Banach spaces and ℬ(X) and ℬ(Y) the algebras of all bounded linear operators on X and Y, respectively. We say that A,B ∈ ℬ(X) quasi-commute if there exists a nonzero scalar ω such that AB = ωBA. We characterize bijective linear maps ϕ : ℬ(X) → ℬ(Y) preserving quasi-commutativity. In fact, such a characterization can be proved for much more general algebras. In the finite-dimensional case the same result can be obtained without the bijectivity assumption.
LA - eng
KW - linear preserver; quasi-commutativity; commutant; quasi-commutant; Banach spaces; bounded linear operators
UR - http://eudml.org/doc/284559
ER -