Year: 2025
Type: article
Abstract: Let S be an operator system sitting in its C∗-envelope C∗min(S). Starting with a pure state on S, let F be the face of state extensions to C∗min(S). The dilation theorem of Davidson-Kennedy shows that the GNS representations corresponding to some of the extreme points of F are boundary representations. We construct an explicit example in which F is an interval and only one of the two extreme points yields a boundary representation.
Source: Journal of Operator Theory
Authors: Kenneth R. Davidson, Michael Hartz
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414580880
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