C*-extreme points of positive operator valued measures.
| Speaker |
B. V. Rajarama Bhat (ISI Bangalore)
|
|---|---|
| When |
Apr 19, 2022
from 04:00 PM to 05:00 PM |
| Where | zoom talk |
| Contact Name | pramila |
| Add event to calendar |
vCal
iCal
|
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.