Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products

Yunhe Chen, and Jiankui Li. "Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products." Studia Mathematica 206.2 (2011): 121-134. <http://eudml.org/doc/285613>.

@article{YunheChen2011,
abstract = {Let 𝓛 be a subspace lattice on a Banach space X and let δ: Alg𝓛 → B(X) be a linear mapping. If ⋁ \{L ∈ 𝓛 : L₋ ⊉ L\}= X or ⋁ \{L₋ : L ∈ 𝓛, L₋ ⊉ L\} = (0), we show that the following three conditions are equivalent: (1) δ(AB) = δ(A)B + Aδ(B) whenever AB = 0; (2) δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) whenever AB + BA = 0; (3) δ is a generalized derivation and δ(I) ∈ (Alg𝓛)'. If ⋁ \{L ∈ 𝓛 : L₋ ⊉ L\} = X or ⋁ \{L₋ : L ∈ 𝓛, L₋ ⊉ L\} = (0) and δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) whenever AB = 0, we show that δ is a generalized derivation and δ(I)A ∈ (Alg𝓛)' for every A ∈ Alg𝓛. We also prove that if ⋁ \{L ∈ 𝓛 : L₋ ⊉ L\} = X and ⋁ \{L₋ : L ∈ 𝓛, L₋ ⊉ L\} = (0), then δ is a local generalized derivation if and only if δ is a generalized derivation.},
author = {Yunhe Chen, Jiankui Li},
journal = {Studia Mathematica},
keywords = {derivation; Jordan derivation; reflexive algebra},
language = {eng},
number = {2},
pages = {121-134},
title = {Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products},
url = {http://eudml.org/doc/285613},
volume = {206},
year = {2011},
}

TY - JOUR
AU - Yunhe Chen
AU - Jiankui Li
TI - Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products
JO - Studia Mathematica
PY - 2011
VL - 206
IS - 2
SP - 121
EP - 134
AB - Let 𝓛 be a subspace lattice on a Banach space X and let δ: Alg𝓛 → B(X) be a linear mapping. If ⋁ {L ∈ 𝓛 : L₋ ⊉ L}= X or ⋁ {L₋ : L ∈ 𝓛, L₋ ⊉ L} = (0), we show that the following three conditions are equivalent: (1) δ(AB) = δ(A)B + Aδ(B) whenever AB = 0; (2) δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) whenever AB + BA = 0; (3) δ is a generalized derivation and δ(I) ∈ (Alg𝓛)'. If ⋁ {L ∈ 𝓛 : L₋ ⊉ L} = X or ⋁ {L₋ : L ∈ 𝓛, L₋ ⊉ L} = (0) and δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) whenever AB = 0, we show that δ is a generalized derivation and δ(I)A ∈ (Alg𝓛)' for every A ∈ Alg𝓛. We also prove that if ⋁ {L ∈ 𝓛 : L₋ ⊉ L} = X and ⋁ {L₋ : L ∈ 𝓛, L₋ ⊉ L} = (0), then δ is a local generalized derivation if and only if δ is a generalized derivation.
LA - eng
KW - derivation; Jordan derivation; reflexive algebra
UR - http://eudml.org/doc/285613
ER -