Abstract
We provide characterizations of convex, compact for the topology of local convergence in measure subsets of non-commutative L1-spaces previously considered for classical L1-spaces. More precisely, if M is a semifinite and σ-finite von Neumann algebra equipped with a distinguished semifinite faithful normal trace τ, P:M∗→L1(M,τ) is the non-commutative Yosida–Hewitt projection, and C is a norm bounded subset of L1(M,τ) that is convex and closed for the topology of local convergence in measure then we isolate the precise conditions on C for which P:C¯w∗→C is compactness preserving, sequentially continuous, or continuous when C¯w∗ is equipped with the weak* topology and C with the topology of local convergence in measure.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
