连续函数空间C(Ω)上的算子和它的表示测度  

The Operators on Spaces of Continuous Functions C(Ω) and Its Representing Measure

作　　者：于素芬[1] 

机构地区：[1]内蒙古大学数学系,内蒙古呼和浩特010021

出　　处：《内蒙古大学学报（自然科学版）》2000年第6期568-571,共4页Journal of Inner Mongolia University：Natural Science Edition

基　　金：内蒙古自然科学基金资助项目!(批准号 990 30 1- 1 )

摘　　要：讨论了连续函数空间 C(Ω )上的 Bartle积分算子与其表示测度之间的关系 .证明了只要μ是非负 Borel测度 ,包含映射 J:C( Ω)→ L1( μ)就是绝对可和算子 ,同时也是 Pietsch积分算子 ,且‖J‖ as=‖J‖ pint=μ( Ω) .而 μ的正则性保证了由 G( E) =χE定义的向量测度 G是Relations between the Bartle integral operators on the continuous function space C(Ω) and their representing measures are discussed.We prove that if μ is a nonnegative Borel measure on Ω, then the natural inclusion J:C(Ω)→L 1(μ) is an absolutely summing operator and a Pietsch integral operator with ‖J‖ as =‖J‖ pint =μ(Ω), and the regularity of μ guarantee that the vector measure G:Σ→L 1(μ), defined by G(E)=χ E, is the representation measure of J.

关 键 词：Bartle积分算法 表示测度 连续函数空间 

分 类 号：O177.2[理学—数学]