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

• Autorzy: Xiaofei Qi , Jinchuan Hou
• Języki publikacji: EN

Abstrakty

EN

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 at zero on Alg ℒ is also obtained, which are not of the above standard form in general.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 197
• Numer: 2
• Strony: 157-169

Daty

wydano

2010

Twórcy

autor

Xiaofei Qi

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

autor

Jinchuan Hou

• Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China

Identyfikatory

DOI

10.4064/sm197-2-3