## Mathematical Physics and Operator Algebras

•  Roy Araiza, Purdue University
•  An Abstract Characterization for Projections in Operator Systems
•  09/21/2020
•  3:00 PM - 3:50 PM
•  Online (virtual meeting)

Given an abstract operator system V it is not clear how one would go about defining the notion of a projection. During this talk I will present an answer and some recent results on this question. This is done by first considering abstract compression operator systems associated with a positive contraction in V and then determining when we have a realization of V in such an abstract compression operator system. It then follows that there is a one-to-one correspondence between abstract and concrete projections, and in particular, that every abstract projection is a concrete projection in the C*-envelope of V. I will then conclude with some applications to quantum information theory. In particular, the study of certain correlation sets. This is joint work with Travis Russell (West Point). Join via Zoom: https://msu.zoom.us/j/95716797501

## Contact

Department of Mathematics
Michigan State University