A Uniform Kadec-klee Property For Symmetric Operator Spaces

Details A Uniform Kadec-klee Property For Symmetric Operator Spaces A Uniform Kadec-klee Property For Symmetric Operator Spaces

1993-01-28

arxiv.org/abs/math/9301201v1

Mathematics

Functional Analysis

Scientific paper

We show that if a rearrangement invariant Banach function space $E$ on the positive semi-axis satisfies a non-trivial lower $q-$ estimate with constant $1$ then the corresponding space $E(\nm)$ of $\tau-$measurable operators, affiliated with an arbitrary semi-finite von Neumann algebra $\nm$ equipped with a distinguished faithful, normal, semi-finite trace $\tau $, has the uniform Kadec-Klee property for the topology of local convergence in measure. In particular, the Lorentz function spaces $L_{q,p}$ and the Lorentz-Schatten classes ${\cal C}_{q,p}$ have the UKK property for convergence locally in measure and for the weak-operator topology, respectively. As a partial converse , we show that if $E$ has the UKK property with respect to local convergence in measure then $E$ must satisfy some non-trivial lower $q$-estimate. We also prove a uniform Kadec-Klee result for local convergence in any Banach lattice satisfying a lower $q$-estimate.

Affiliated with

Also associated with

No associations

Rating

A Uniform Kadec-klee Property For Symmetric Operator Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Uniform Kadec-klee Property For Symmetric Operator Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Uniform Kadec-klee Property For Symmetric Operator Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-46343