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

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.