The AM-compactness Of Dunford-pettis Operators

AM-compact and Dunford-Pettis operators are two kinds of important operators on Banach lattice,The problems about the lattice properties, dominated properties,and conjugate properties of AM-compact operators are discussed in this thesis,the AM-compactness of Dunford-Pettis operator on Banach Lattice are also included.In the first part,the backgrounds and preliminary about AM-compact and Dunford-Pettis operators are given briefly,which of course are the base of the thesis.In the second part,it's devoted to talking about the lattice properties, dominated properties,and the conjugate properties of the AM-compact operators. Firstly,a sufficient condition is given for those AM-compact operators which have a AM-compact modulus.Secondly,a mistake has been found in the proof of one theorem in[10]about the dominated property of AM-compact operators.At last,a necessary condition is given for those operators whose conjugate are AM-compact which can induced that the operators themselves are AM-compact.In the third part,on the base of my mentor's research,some sufficient conditions are given for those Dunford-Pettis operators which are AM-compact operators,moreover,it's been proved that when E' is discrete and F is an AL-space,then every regular operator is Dunford-Pettis if and only if it is a AM-compact operator itself.In the forth part,a note is given to illustrate the fact the characterization of disjiont preserving operator by matrix is deeply dependent on the order in the space.