Pseudodifferential operators in strict deformation quantization

Abstract: Most of the talk will be about old results of H. O. Cordes, Marcela Merklen and myself about characterizations of pseudodifferential operators as smooth vectors for actions of the Heisenberg group. Then I will announce related results recently obtained with Rodrigo Cabral and Michael Forger about a class of pseudodifferential operators with $C^*$-algebra-valued symbols introduced by M. Rieffel in his construction of a "strict deformation quantization" for a $C^*$-algebra with an action of $R^n$. We have proven the uniqueness of the $C^*$-norm for Rieffel's (non complete) algebra and have also proven a conjecture of Rieffel which characterizes his pseudodifferential operators as the smooth vectors for an action of the Heisenberg group.

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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