Characterization of Jordan derivations on 𝒥-subspace lattice algebras

• Autorzy: Xiaofei Qi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47L35: Nest algebras, CSL algebras
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 210
• Numer: 1
• Strony: 17-33

Daty

wydano

2012

Twórcy

autor

Xiaofei Qi

• Department of Mathematics, Shanxi University, 030006 Taiyuan, P.R. China

Identyfikatory

DOI

10.4064/sm210-1-2