纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2011年
5期
650-655
,共6页
弱极限集%弱极限算子%算子理想
弱極限集%弱極限算子%算子理想
약겁한집%약겁한산자%산자이상
weak limited set%weak limited operator%operator ideal
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．
為瞭進一步研究Banach空間中集閤的緊緻性，受極限集與極限算子定義的啟髮，給齣瞭弱極限集與弱極限算子的定義，得到瞭它們的等價刻畫，利用空間結構與算子理想的互動關繫證明瞭弱極限算子全體是Pietsch意義下的閉滿射算子理想．
위료진일보연구Banach공간중집합적긴치성，수겁한집여겁한산자정의적계발，급출료약겁한집여약겁한산자적정의，득도료타문적등개각화，이용공간결구여산자이상적호동관계증명료약겁한산자전체시Pietsch의의하적폐만사산자이상．
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.
