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SUMMARY:Absolutely dilatable module maps - Lyudmila  Turowska (Chalmers Un
 iversity of Technology)
DTSTART:20241205T160000Z
DTEND:20241205T170000Z
UID:TALK218653@talks.cam.ac.uk
DESCRIPTION:I&nbsp\;will discuss the notion of absolute dilation for maps 
 on von Neumann algebras\, focusing primarily on maps on B(H) with an addit
 ional modularity condition. The notion was recently defined and studied by
  C. Duquet and C. Le Merdy. They characterized dilatable Schur multipliers
 . We extend the results by replacing the requirement of being Schur by bei
 ng modular over arbitrary von Neumann algebra\, instead of maximal abelian
  selfadjoint algebra. &nbsp\;&nbsp\;&nbsp\;Such maps &nbsp\;&nbsp\;are cha
 racterized by the existence of a tracial von Neumann algebra (N\, &tau\;)\
 , called an ancilla\, and a certain unitary operator. Different types of a
 ncillas (abelian\, finite-dimensional\, etc.) lead to the definition of lo
 cal\, quantum\, approximate quantum\, and quantum commuting dilatable maps
 \, and I will discuss the relationships between these types. The motivatio
 n to study different types of dilations comes from Quantum Information The
 ory.\nThe talk is based on a project with A. Chatzinikolaou and I. G. Todo
 rov.
LOCATION:Seminar Room 1\, Newton Institute
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