Additive maps derivable at some points on J-subspace lattice algebras

作者：Hou Jinchuan^*; Qi Xiaofei

来源：Linear Algebra and Its Applications, 2008, 429(8-9): 1851-1863.

DOI：10.1016/j.laa.2008.05.013

• J-subspace lattice algebra
• additive maps derivable at zero point
• linear maps derivable at unit operator

Let L be a J-subspace lattice on a real or complex Banach space X with dim X > 2 and AlgL be the associated J-subspace lattice algebra. Let A : AlgL --> AlgL be an additive map. It is shown that, if delta is derivable at zero point, i.e., delta(A B) = delta(A) B + A delta(B) whenever AB = 0, then delta(A) = tau(A) + lambda A, for all A, where tau is an additive derivation and X is a scalar; if delta is generalized derivable at zero point, i.e., delta(AB) = delta(A) B + A delta(B) - A delta(I) B whenever AB = 0, then delta is a generalized derivation. It is also shown that, if X is complex, then every linear map derivable at unit operator on AlgL is a derivation.

• 出版日期2008-10-16
• 单位太原理工大学; 山西大学