The Order Continuity of the Regular Norm on Regular Operator Spaces

الملخص EN

We present here some sufficient conditions for the regular norm on ℒr(E,F) to be order continuous, and for (ℒr(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 ℒr(E,F) is an Lp-space and is lattice isomorphic to an Lp-space for 1

Some related results are also obtained.