Projective positivity of the function systems

Abstract: The present talk is devoted to the projective positivity in the category of function systems. It is an operator positivity occurred in the quantization problems of the operator systems. It turns out that every $∗$-(poly)normed topology compatible with a duality results in the (local) projective positivity given by a filter base of the unital cones with its separated intersection. We describe the (local) projective positivity of the (local) $L^{p}$-spaces given by a bounded (or unbounded) positive Radon measure on a locally compact topological space. The geometry of the related state spaces is described in the case of $L^{p}$-spaces, Schatten matrix spaces, and $L^{p}$-spaces of a finite von Neumann algebra.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | 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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