Categories of Hilbert spaces

Abstract: Hilbert spaces form one category with bounded operators and another category with contractions. I will present axioms for each of these two categories. These axioms are interesting because they make no explicit reference to the real number system. The proof appeals to Soler's theorem and to the theory of dagger categories, as well as to a few familiar results from operator theory.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

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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