Banach格上的b-几乎极限算子

为了进一步研究Banach格上算子的性质,受b-序有界集和几乎极限集定义的启发,给出了b-几乎极限算子的定义,研究了该算子与b-AM-紧算子(几乎极限算子,序-几乎极限算子)间的关系;利用几乎极限算子的控制性证明了b-几乎极限算子的控制性.

b-almost limited operators on Banach lattices

For the further study of the property of operators on Banach lattices,this paper gives the MAC of b-almost limited operators in light of the definition of b-order bounded set and almost limited set,and studies the relationship between b-almost limited operator and b-AM-compact operator(almost limited operator,order-almost limited operator). By means of the dominated property of almost limited operators,it has proved that the b-almost limited operator has the dominated property.