The Order Continuity of the Regular Norm on Regular Operator Spaces - Zi Li Chen; Ying Feng; Jin Xi Chen (Abstract and Applied Analysis)
We present here some sufficient conditions for the regular norm on to be order continuous, and for () to be a KB-space. In particular we deduce a characterization of the order continuity of the regular norm using L- and M-weak compactness of regular operators. Also we characterize when the space is an -space and is lattice isomorphic to an -space for . Some related results are also obtained.