B-L-Weakly Compect Operators On Banach Lattices

Based on the proposed method of b-weakly compact and b-AM-compact operators, we consider a new class of operators, so called b-L-weakly compact operator, which map b-order bounded sets into L-weakly compact sets. This paper is denoted to its fundermental properties, and establish some relatinships among b-L-weakly compact operators and other special operators.Firstly, the basic properties of b-L-weakly compact operators are discussed, such as formed space property, algebra two sides ideal. Then, we study the characterization of b-L-weakly compact operators, and discuss the conditions under which each linearly bounded operator between Banach lattices is b-L-weakly compact. At last, This paper discusses the controlity and duality property of b-L-weakly compact operator.Secondly, this paper makes a deep research among b-L-weakly compact, L-(M-)weakly compact, order L-weakly compact operator, and establish conditions under which these operators is the same as b-L-weakly compact operator. At last, we establish the necessary and sufficient conditions under which each b-weakly compact operators is b-L-weakly compact.