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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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
121-134
Opis fizyczny
Daty
wydano
2011
Twórcy
autor
- Department of Mathematics, East China University of, Science and Technology, Shanghai 200237, People's Republic of China
autor
- Department of Mathematics, East China University of, Science and Technology, Shanghai 200237, People's Republic of China
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm206-2-2