From spectral triples in NCG to Grothendieck's inequalities in the theory of finite rank matrices

Abstract: While studying properties of a spectral triple, I realized that the Schur product - or entry wise product of infinite matrices -- has a nice Stinespring representation as a completely bounded bilinear operator. On the other hand it is well known that Grothendieck's inequality on bilinear forms has a dual counterpart, which describes certain properties of Schur multipliers. It turned out that the theory of operator spaces and completely bounded multilinear maps form a nice background to present some classical and some new results on both the Schur product and on Grothendieck's inequalities. Part of this will be extended to the non commutative Grothendieck inequality too.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides | video )

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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