Weakly compact subsets of symmetric operator spaces. (English) Zbl 0767.46040
Summary: Under natural conditions it is shown that the rearrangement invariant hull of a weakly compact subset of a properly symmetric Banach space of measurable operators affiliated with a semi-finite von Neumann algebra is again relatively weakly compact.
MSC:
46L51 | Noncommutative measure and integration |
46L53 | Noncommutative probability and statistics |
46L54 | Free probability and free operator algebras |
46A50 | Compactness in topological linear spaces; angelic spaces, etc. |
47L07 | Convex sets and cones of operators |
Keywords:
rearrangement invariant hull of a weakly compact subset; relatively weakly compact; properly symmetric Banach space of measurable operators affiliated with a semifinite von Neumann algebraReferences:
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