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

• Autorzy: Yunhe Chen , Jiankui Li
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47L35: Nest algebras, CSL algebras
• 17B40: Automorphisms, derivations, other operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 206
• Numer: 2
• Strony: 121-134

Daty

wydano

2011

Twórcy

autor

Yunhe Chen

• Department of Mathematics, East China University of, Science and Technology, Shanghai 200237, People's Republic of China

autor

Jiankui Li

• Department of Mathematics, East China University of, Science and Technology, Shanghai 200237, People's Republic of China

Identyfikatory

DOI

10.4064/sm206-2-2