Radon－Nikodym性质与Riesz可表示算子

The Radon-Nikodym Property and the Riesz Representable Operator

本文证明了如下定理：设ｘ是Ｆｒｅｃｈｅｔ空间，（Ｓ，β，μ）是有限测度空间，那么Ｘ关于（Ｓ，β，μ）具有Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质当且仅当任给Ｔ∈Ｌ（Ｌ（μ），ｘ）是Ｒｉｅｓｚ可表示的。

In this paper ,the following theorem has been proved :Let X be a Frechet spece and let(S,β,μ)be a finite measure spece. Then X has the Radon-Nikodym property with respect to(S,β,μ)if and only if each T∈L(L(μ),X) is Riesz representable.