| The operator property is a famous problem in the history of operator theory. This dissertation is devoted to the study of properties of several special operators on Banach lattice and divided into the following five parts:The first part is devoted to the AM-compact operators factor through Banach lattice with order continuous norm and one AM-compact factor. As consequence, we obtain some interesting results on positive AM-compact operators. And the similar question for Dunford-Pettis operator is also considered.Main results are included in the second part, firstly, we give several characterizations of b-AM-compact operators. Secondly, we study several properties about the problems of domination in the class of positive b-AM-compact operators. Moreover, we present the condition that if the dual operator T':F'→E'is b-AM-compact, then the positive operator T:E→F is b-AM-compact. We also give the condition for the adjoint operators of each b-AM-compact operators being also b-AM-compact. Finally, several equivalent conditions characterizing when the space of regular b-AM-compact operator is Dedekindσ-complete are given.In the third part, we present some necessary and sufficient conditions for positive Dunford-Pettis operators being L-weakly compact. We also give a necessary condition under which each positive Dunford-Pettis operator is M-weakly compact.In the fourth part, we present some necessary and sufficient conditions for positive semi-compact operators being L-weakly compact and M-weakly compact respectively.Finally, we investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We present a necessary and sufficient condition under which each positive semi-compact operator is b-weakly compact.■...
|
PDF Full Text Request