# Prairie Mathematics Colloquium

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Thu., Nov. 23, 2023 2:30 p.m.
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Location: Live Stream
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**Speaker: **Raphaël Clouâtre, University of Manitoba

**Title: **Pure states on operator algebras

**Zoom Link: **https://usask-ca.zoom.us/j/96349416490?pwd=MTg2dDZZNXdOMlJESEs2Ly9WL1ZoZz09

**Abstract: **

Let B be a normed space and let A be a subspace. When does a continuous linear functional on A admit a unique norm-preserving extension to B? If A and B are C*-algebras and the functional is a so-called pure state, this question was at the heart of a long-standing conjecture of Kadison and Singer from 1959, which was eventually verified in 2015 by Marcus, Spielman and Srivastava. In this talk I will explore the corresponding problem for pure states on subspaces of C*-algebras. I will explain how this is non-trivial even for familiar choices of B, such as the continuous functions on some compact space, or the n x n matrices. I will attempt to clarify this issue using a non-commutative counterpart to the classical notion of peak point from function theory.

See: Prairie Mathematics Colloquium

This event is supported by PIMS.