【作者】 林鸿钊；

【导师】 钟怀杰；

【作者基本信息】 福建师范大学 ， 基础数学， 2005， 硕士

【摘要】 本文的主要工作是在收集、整理前人研究成果的基础上,从(Pietsch意义下)广义算子理想、广义空间理想的角度去研究极限算子及其相关问题,用新的方法、从新的角度去重新证明、认识一些漂亮结论.§1和§2开列了有关极限集和极限算子的主要成果,证明了极限算子全体LO是真闭满射算子理想,并且(L,LO)=LO.这里L表示有界线性算子全体(以下类同).§3主要是说明GP空间全体(?)P是广义空间理想. §4是用研究极限集、极限算子的方法来讨论极限集与极限算子的弱化-弱极限集与弱极限算子,证明了弱极限算子全体WUNO是闭满射算子理想, (L,WUNO)=WUNO.§5是将有界线性算子全体B(E,F)中的极限算子全体LO(E,F)作为Banach空间来研究。将Kalton的证明方法从B(E,F)中紧算子全体K(E,F)推广到LO(E,F),得到了一些平行的结果.更多还原

【Abstract】 On the basis of collecting and rearranging most of the previous results , we study the limited operator and relavent problems in the view of operator ideals and space ideals in the sense of Pietsh. In addition, we also give new proof to several existing results with new method or from new angle. Section 1 and section 2 give the main results about the limited set and the limited operator. Further more,we prove that the set of all the limited operators LCD is a real and closed surjective operator ideal and that (L, LO) = LO, where L is the set of all the bounded linear operators. Section 3 mainly points it out that GP is a space ideal. In section 4 ,we use the method by which we discuss the limited set and the limited operator to discuss the weakly limited set and the weakly limited operator, which are respectively weaker than the limited set and the limited operator. And we also prove that the set of all the weakly limited operators WUNO is a closed surjective operator ideal and that (L, WUNO) = WUNO. In section 5, we study the set of all the limited operators LO(E, F) as a Banach space . Generalizing Kalton’s method from the set of all the compact operators K(E, F) to LO(E,F), we get some parallel results.更多还原