Linear maps Lie derivable at zero on 𝒥-subspace lattice algebras

Xiaofei Qi, and Jinchuan Hou. "Linear maps Lie derivable at zero on 𝒥-subspace lattice algebras." Studia Mathematica 197.2 (2010): 157-169. <http://eudml.org/doc/285795>.

@article{XiaofeiQi2010,
abstract = {A linear map L on an algebra is said to be Lie derivable at zero if L([A,B]) = [L(A),B] + [A,L(B)] whenever [A,B] = 0. It is shown that, for a 𝒥-subspace lattice ℒ on a Banach space X satisfying dim K ≠ 2 whenever K ∈ 𝒥(ℒ), every linear map on ℱ(ℒ) (the subalgebra of all finite rank operators in the JSL algebra Alg ℒ) Lie derivable at zero is of the standard form A ↦ δ (A) + ϕ(A), where δ is a generalized derivation and ϕ is a center-valued linear map. A characterization of linear maps Lie derivable at zero on Alg ℒ is also obtained, which are not of the above standard form in general.},
author = {Xiaofei Qi, Jinchuan Hou},
journal = {Studia Mathematica},
language = {eng},
number = {2},
pages = {157-169},
title = {Linear maps Lie derivable at zero on 𝒥-subspace lattice algebras},
url = {http://eudml.org/doc/285795},
volume = {197},
year = {2010},
}

TY - JOUR
AU - Xiaofei Qi
AU - Jinchuan Hou
TI - Linear maps Lie derivable at zero on 𝒥-subspace lattice algebras
JO - Studia Mathematica
PY - 2010
VL - 197
IS - 2
SP - 157
EP - 169
AB - A linear map L on an algebra is said to be Lie derivable at zero if L([A,B]) = [L(A),B] + [A,L(B)] whenever [A,B] = 0. It is shown that, for a 𝒥-subspace lattice ℒ on a Banach space X satisfying dim K ≠ 2 whenever K ∈ 𝒥(ℒ), every linear map on ℱ(ℒ) (the subalgebra of all finite rank operators in the JSL algebra Alg ℒ) Lie derivable at zero is of the standard form A ↦ δ (A) + ϕ(A), where δ is a generalized derivation and ϕ is a center-valued linear map. A characterization of linear maps Lie derivable at zero on Alg ℒ is also obtained, which are not of the above standard form in general.
LA - eng
UR - http://eudml.org/doc/285795
ER -