Dilations, Completely Positive Maps and Geometry
This book introduces the dilation theory of operators on Hilbert spaces and its relationship to complex geometry. Classical as well as very modern topics are covered in the book. On the one hand, it introduces the reader to the characteristic function, a classical object used by Sz.-Nagy and Foias a...
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| 格式: | 電子 電子書 |
| 語言: | 英语 |
| 出版: |
Singapore :
Springer Nature Singapore : Imprint: Springer,
2023.
|
| 版: | 1st ed. 2023. |
| 叢編: | Texts and Readings in Mathematics,
84 |
| 主題: | |
| 在線閱讀: | https://doi.org/10.1007/978-981-99-8352-0 |
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| 100 | 1 | |a Bhat, B.V. Rajarama. |e author. |0 (orcid)0000-0002-4614-8890 |1 https://orcid.org/0000-0002-4614-8890 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Dilations, Completely Positive Maps and Geometry |h [electronic resource] / |c by B.V. Rajarama Bhat, Tirthankar Bhattacharyya. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Singapore : |b Springer Nature Singapore : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XI, 229 p. 3 illus.). | ||
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| 341 | 0 | |b Single logical reading order |2 onix | |
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| 490 | 1 | |a Texts and Readings in Mathematics, |x 2366-8725 ; |v 84 | |
| 505 | 0 | |a Dilation for One Operator -- C*-Algebras and Completely Positive Maps -- Dilation Theory in Two Variables - The Bidisc -- Dilation Theory in Several Variables - the Euclidean Ball -- The Euclidean Ball - The Drury Arveson Space -- Dilation Theory in Several Variables - The Symmetrized Bidisc -- An Abstract Dilation Theory. | |
| 520 | |a This book introduces the dilation theory of operators on Hilbert spaces and its relationship to complex geometry. Classical as well as very modern topics are covered in the book. On the one hand, it introduces the reader to the characteristic function, a classical object used by Sz.-Nagy and Foias and still a topic of current research. On the other hand, it describes the dilation theory of the symmetrized bidisc which has been developed mostly in the present century and is a very active topic of research. It also describes an abstract theory of dilation in the setting of set theory. This was developed very recently. A good portion of the book discusses various geometrical objects like the bidisc, the Euclidean unit ball, and the symmetrized bidisc. It shows the similarities and differences between the dilation theory in these domains. While completely positive maps play a big role in the dilation theory of the Euclidean unit ball, this is not so in the symmetrized bidisc for example. There, the central role is played by an operator equation. Targeted to graduate students and researchers, the book introduces the reader to different techniques applicable in different domains. | ||
| 532 | 8 | |a Accessibility summary: This PDF does not fully comply with PDF/UA standards, but does feature limited screen reader support, described non-text content (images, graphs), bookmarks for easy navigation and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Operator theory. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 0 | |a Geometry. | |
| 650 | 1 | 4 | |a Operator Theory. |
| 650 | 2 | 4 | |a Functional Analysis. |
| 650 | 2 | 4 | |a Geometry. |
| 700 | 1 | |a Bhattacharyya, Tirthankar. |e author. |0 (orcid)0000-0002-9566-0815 |1 https://orcid.org/0000-0002-9566-0815 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 830 | 0 | |a Texts and Readings in Mathematics, |x 2366-8725 ; |v 84 | |
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| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||