Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

Characterization of Jordan derivations on 𝒥-subspace lattice algebras

Xiaofei Qi — 2012

Studia Mathematica

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...

Linear maps Lie derivable at zero on 𝒥-subspace lattice algebras

Xiaofei Qi;  Jinchuan Hou — 2010

Studia Mathematica

A linear map L on an algebra is said to be Lie derivable at zero if L([A,B]) = [L(A),B] + [A,L(B)] whenever [A,B] = 0. It is shown that, for a 𝒥-subspace lattice ℒ on a Banach space X satisfying dim K ≠ 2 whenever K ∈ 𝒥(ℒ), every linear map on ℱ(ℒ) (the subalgebra of all finite rank operators in the JSL algebra Alg ℒ) Lie derivable at zero is of the standard form A ↦ δ (A) + ϕ(A), where δ is a generalized derivation and ϕ is a center-valued linear map. A characterization of linear maps Lie derivable...

Page 1

Download Results (CSV)