Characterization of Jordan derivations on 𝒥-subspace lattice algebras

Xiaofei Qi. "Characterization of Jordan derivations on 𝒥-subspace lattice algebras." Studia Mathematica 210.1 (2012): 17-33. <http://eudml.org/doc/285544>.

@article{XiaofeiQi2012,
abstract = {Let 𝓛 be a 𝒥-subspace lattice on a Banach space X and Alg 𝓛 the associated 𝒥-subspace lattice algebra. Assume that δ: Alg 𝓛 → Alg 𝓛 is an additive map. It is shown that δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) for any A,B ∈ Alg 𝓛 with AB + BA = 0 if and only if δ(A) = τ(A) + δ(I)A for all A, where τ is an additive derivation; if X is complex with dim X ≥ 3 and if δ is linear, then δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) for any A,B ∈ Alg 𝓛 with AB + BA = I if and only if δ is a derivation.},
author = {Xiaofei Qi},
journal = {Studia Mathematica},
keywords = {J-subspace lattice algebras; Jordan derivations; derivations; derivable maps},
language = {eng},
number = {1},
pages = {17-33},
title = {Characterization of Jordan derivations on 𝒥-subspace lattice algebras},
url = {http://eudml.org/doc/285544},
volume = {210},
year = {2012},
}

TY - JOUR
AU - Xiaofei Qi
TI - Characterization of Jordan derivations on 𝒥-subspace lattice algebras
JO - Studia Mathematica
PY - 2012
VL - 210
IS - 1
SP - 17
EP - 33
AB - Let 𝓛 be a 𝒥-subspace lattice on a Banach space X and Alg 𝓛 the associated 𝒥-subspace lattice algebra. Assume that δ: Alg 𝓛 → Alg 𝓛 is an additive map. It is shown that δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) for any A,B ∈ Alg 𝓛 with AB + BA = 0 if and only if δ(A) = τ(A) + δ(I)A for all A, where τ is an additive derivation; if X is complex with dim X ≥ 3 and if δ is linear, then δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) for any A,B ∈ Alg 𝓛 with AB + BA = I if and only if δ is a derivation.
LA - eng
KW - J-subspace lattice algebras; Jordan derivations; derivations; derivable maps
UR - http://eudml.org/doc/285544
ER -