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SUMMARY:Gilles Pisier (Texas A&M)
DTSTART:20210609T160000Z
DTEND:20210609T165000Z
DTSTAMP:20260423T004516Z
UID:Opalg21/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Opalg21/9/">
 From injectivity to approximation properties for von Neumann algebras</a>\
 nby Gilles Pisier (Texas A&M) as part of Conference on operator algebras a
 nd related topics in Istanbul\, 2021\n\n\nAbstract\nA von Neumann algebra 
 M is called injective if there is a projection P:B(H) -> M with ||P||= 1. 
 This is the analogue for von Neumann algebras of amenability for discrete 
 groups\, and it notoriously fails when M = M(F) is the von Neumann algebra
  of a non-commutative free group F. We will introduce the class of ''seemi
 ngly injective'' von Neumann algebras. This includes M(F). We show that M 
 is seemingly injective iff it has the (matricial) weak* positive metric ap
 proximation property (AP in short). This is parallel to Connes's character
 ization of injectivity by the weak* completely positive AP. We show that M
 (F) is isomorphic to B(H) as Banach spaces when F is countable. Lastly we 
 discuss several open questions that might be related to Kazhdan's property
  (T) for groups.\n
LOCATION:https://researchseminars.org/talk/Opalg21/9/
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