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C*-extreme points of positive operator valued measures.

B. V. Rajarama Bhat (ISI Bangalore)
B. V. Rajarama Bhat (ISI Bangalore)
When Apr 19, 2022
from 04:00 PM to 05:00 PM
Where zoom talk
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Abstract: We study the C*-convexity structure of normalized positive operator valued measures (POVMs) on measurable spaces. In particular, it is seen that unlike extreme points under classical convexity, C*-extreme points of normalized POVMs on countable spaces (in particular for finite sets) are always spectral measures (normalized projection valued measures). More generally it is shown that atomic C*-extreme points are spectral. As an application it is shown that a map on any commutative unital C*-algebra with countable spectrum (in particular C^n) is C*-extreme in the set of unital completely positive maps if and only if it is a unital *-homomorphism. This settles a problem which has been open since 1997.

This talk is based on a joint work with Tathagata Banerjee and Manish Kumar.

Youtube link to the recording

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