The Order Continuity of the Regular Norm on Regular Operator Spaces. (9th June 2013) - Chen, Zi Li; Feng, Ying; Chen, Jin Xi
Abstract : We present here some sufficient conditions for the regular norm on ℒ r ( E, F ) to be order continuous, and for (ℒ r ( E, F ), ∥ · ∥ r ) 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 ℒ r ( E, F ) is an L p -space and is lattice isomorphic to an L p -space for 1 < P < ∞ . Some related results are also obtained.