On boundary representations
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| Title: | On boundary representations |
|---|---|
| Authors: | Davidson, Kenneth R., Hartz, Michael |
| Source: | Journal of Operator Theory. 94:23-34 |
| Publication Status: | Preprint |
| Publisher Information: | Theta Foundation, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Mathematics - Functional Analysis, 46L07 (Primary), 47A20, 46E22, 47L55 (Secondary), Mathematics - Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA), Functional Analysis (math.FA) |
| Description: | 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. |
| Document Type: | Article |
| ISSN: | 1841-7744 0379-4024 |
| DOI: | 10.7900/jot.2023aug08.2439 |
| DOI: | 10.48550/arxiv.2308.04919 |
| Access URL: | http://arxiv.org/abs/2308.04919 |
| Rights: | arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....a561e808c722c63d8c9afceaf24b3a5b |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | 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. |
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| ISSN: | 18417744 03794024 |
| DOI: | 10.7900/jot.2023aug08.2439 |