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:

本文研究算子代数上的(α, β)-导子的空间实现性。设A是B(X)的子代数，α和β是A上的自同构，δ是从A到B(X)的(α, β)- 导子。如果δ是传递的、自反的(α, β)-导子，则δ是拟空间实现的也就是说， 存在一个稠定义的闭线性算子T使得Dom(T)是δ(A）-不变子流形以及δ(A)x = (Tβ(A)-α(A) T)x 成立。如果δ是传递的、自反的有界(α, β)-导子，而且A的范数闭包包含一个极小左理想，则δ是空间实现的，而且其实现元在相差一个常数因子的条件下是唯一的.

Abstract:

SThe topic of the present paper is the spatiality of (α, β)-derivations of operator algebras. Suppose that X is a Banach space, A is a subalgebra of B(X) and α, β are automorphisms on B(X). It is shown that any reflexive transitive (α, β)-derivation is quasi-spatial. If the norm closure of A contains a nonzero minimal left ideal, then a bounded reflexive transitive (α, β)-derivation δ from A into B(X) is spatial and the implementation T of δ is unique only up to an additive constant.