算子值测度与函数的积分  

INTEGRATIONS OF OPERATOR-VALUED MEASURES AND FUNCTIONS

作　　者：魏常果[1] 

机构地区：[1]曲阜师范大学数学系,山东省曲阜市273165

出　　处：《曲阜师范大学学报（自然科学版）》2001年第2期23-27,共5页Journal of Qufu Normal University(Natural Science)

摘　　要：引入了算子测度和算子值函数的σ_积分 ;证明了L(B(X ,R) ;M)中的任一算子可以表示成X上的σ_弱有界算子测度 ;并给出了σ_弱积分存在的条件及σ_弱算子拓扑下的控制收敛定理 .最后讨论了算子值函数的Bochner积分 .The σ-weak integrations of operator measures and operator-valued functions are introduced. It is proved that any element in L(B(X,R);M) can be represented as a σ-weakly bounded operator measure on X; and the condition of σ-weak integral's existence is given. The Dominated Convergence Theorem under the σ-weak operator topology is also given. At last, the Bochner integral of operator-valued functions is considered.

关 键 词：σ-弱积分 BOCHNER积分 算子值函数 算子代数 

分 类 号：O177.8[理学—数学]