同济大学学报（自然科学版）2013，Vol.41Issue(2)：293-298,6.DOI:10.3969/j.issn.0253-374x.2013.02.024
算子代数上的(α,β)-导子的空间实现性
Spatiality of (α, β)-derivations of Operator Algebras in Banach Spaces
摘要
Abstract
The spatiality of (α, β)-derivations of operator algebras is discussed. Suppose that X is a Banach space, is a subalgebra of B(X) and α,/β are automorphisms on B(X), δ is an (α,β)-derivation from si into B(X). It is shown that any reflexive transitive (α, β)-derivation is quasi-spatial, that is, there is a densely defined, closed operator T with domain Dom(T) such that β(A)(Dom(T))∈Dom(T) and δ(A)χ = (Tβ(A)-α(A)T)x for any A∈ and x∈ Dom(T). If the norm closure of contains a nonzero minimal left ideal, then a bounded reflexive transitive (α,β)-derivation δ from A into B(X) is spatial and implemented uniquely, that is, there exists T∈B(X) such that δ(A) = Tα(A)—α(A)T for each A ∈, and the implementation T of δ is unique only up to an additive constant.关键词
(α,β)-导子/空间实现性/拟空间实现性Key words
(α,β)-derivation/ spatiality/ quasi-spatiality分类
数理科学引用本文复制引用
陈全园,方小春..算子代数上的(α,β)-导子的空间实现性[J].同济大学学报（自然科学版）,2013,41(2):293-298,6.基金项目
国家自然科学基金(11071188) （11071188）
江西省自然科学基金(20122BAB201016) （20122BAB201016）
