Riesz表现定理的向量值形式  

Vector-valued form of Riesz’s representation theorem

作　　者：汪成咏[1] 王序岩 WANG Chengyong;WANG Xuyan(Department of Mathematics,Beijing Jiaotong University,Beijing 100044)

机构地区：[1]北京交通大学数学系,北京100044

出　　处：《首都师范大学学报（自然科学版）》2022年第4期8-14,共7页Journal of Capital Normal University：Natural Science Edition

摘　　要：为了刻画低维向量值函数空间上乘子的特征,导出了从C_(0)(Ω,H)到H、从C_(0)(Ω,H)到C、从C_(0)(Ω)到H的有界线性算子的表现定理,把闭区间上的连续函数空间上的有界线性泛函的Riesz表现定理推广到局部紧的Hausdorff空间上,得到定义域是Hausdorff空间.值域是Banach空间的向量值积分的Riesz表现定理.文中的Ω表示局部紧的Hausdorff空间.In order to characterize the multiplier in the space of low-dimensional vector-valued functions,this paper derive the expression theorems of bounded operators from C_(0)(Ω,H) to H,from C_(0)(Ω,H) to C,and from C_(0)(Ω) to H. This paper extend the Riesz representation theorem of bounded functional on continuous function spaces over closed intervals to locally compact Hausdorff spaces,and obtain the Riesz representation theorem of vector-valued integrals over Banach spaces whose domain is Hausdorff space and range is Banach space. The Ω in this article represents a locally compact Hausdorff space.

关 键 词：有界线性算子 HAUSDORFF空间 Riesz表现定理 向量测度 

分 类 号：O177.1[理学—数学] O177.2[理学—基础数学]