St. Frunza"3 laid the foundation of-duality theorem for decomposable operators. He proved that if y￡J?(X) is a 2-decomposable operator, then T* is also a 2-decomposable operator. His proof is fundamental, but it...St. Frunza"3 laid the foundation of-duality theorem for decomposable operators. He proved that if y￡J?(X) is a 2-decomposable operator, then T* is also a 2-decomposable operator. His proof is fundamental, but it is rather complicated. Here we give a very simple proof, using Dieudonn^’s duality theorem.Wang Shengwang proved that if T* is a decomposable operator, and F a closed set, then -STJ.^) is weak* closed. In this paper we prove if T* has the single-valued extension property, then xt*(f~) is weak* closed whenever it is closed in the strong topology.展开更多
文摘St. Frunza"3 laid the foundation of-duality theorem for decomposable operators. He proved that if y￡J?(X) is a 2-decomposable operator, then T* is also a 2-decomposable operator. His proof is fundamental, but it is rather complicated. Here we give a very simple proof, using Dieudonn^’s duality theorem.Wang Shengwang proved that if T* is a decomposable operator, and F a closed set, then -STJ.^) is weak* closed. In this paper we prove if T* has the single-valued extension property, then xt*(f~) is weak* closed whenever it is closed in the strong topology.
