𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Additive maps derivable at some points on -subspace lattice algebras

✍ Scribed by Jinchuan Hou; Xiaofei Qi

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
151 KB
Volume
429
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

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 δ : AlgL → AlgL be an additive map. It is shown that, if δ is derivable at zero point, i.e., δ(AB) = δ(A)B + Aδ(B) whenever AB = 0, then δ(A) = τ (A) + λA, ∀A, where τ is an additive derivation and λ is a scalar; if δ is generalized derivable at zero point, i.e., δ(AB) = δ(A)B + Aδ(B) -Aδ(I )B whenever AB = 0, then δ 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.

📜 SIMILAR VOLUMES

Generalized derivable mappings at zero p
Generalized derivable mappings at zero point on some reflexive operator algebras
✍ Jun Zhu; Changping Xiong 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 237 KB

Let A be a subalgebra with the unit operator I in B(H ), we say that a linear mapping ϕ from A into B(H ) is a generalized derivable mapping at zero point if ϕ(ST ) = ϕ(S)T + Sϕ(T ) -Sϕ(I )T for any S, T ∈ A with ST = 0. In this paper, we show the following main result: every norm-continuous general