Banach空间中极限集与极限算子的弱化

The weakness of limited set and limited operator in Banach spaces

为了进一步研究Banach空间中集合的紧致性,受极限集与极限算子定义的启发,给出了弱极限集与弱极限算子的定义,得到了它们的等价刻画,利用空间结构与算子理想的互动关系证明了弱极限算子全体是Pietsch意义下的闭满射算子理想.

For the further study of the set compactness on Banach spaces, we give the definition of weak limited set and weak limited operator in light of the definition of limited set and the limited operator, and obtain their equivalent characterization respectively. By means of the interaction between Banach spaces structure and operator ideals, it was proved that all weak limited operators between Banach spaces constitute a closed surjective general operator ideal in the sense of Pietsch.