向量测度的算子分解

Operator Decomposition of Vector Measures

利用向量测度与算子的一一对应关系,给出可列可加测度的算子表示,并进一步由推广的YosidaHewitt定理证明定义在B(Ω,Σ)=span{χA,A∈Σ}上的取值于自反空间X的算子,可唯一分解成w*-范序列连续算子与纯连续算子之和.

Using the isometrim between vector measures and operators, we give the operator representation for countably additive measures, then by applying extended Yosida-Hewitt theorem we show that a operator, which defined on B（Ω,Σ） =span{XA,A∈Σ} and valued in the reflexive Banach space, X can be uniquely decomposed into the sum of a ω＊-norm sequentially continuous operator and a purely continuous operator.