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Record Nr. |
UNINA9910831002203321 |
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Autore |
Bhat B. V. Rajarama |
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Titolo |
Dilations, Completely Positive Maps and Geometry / / by B.V. Rajarama Bhat, Tirthankar Bhattacharyya |
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Pubbl/distr/stampa |
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Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023 |
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ISBN |
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Edizione |
[1st ed. 2023.] |
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Descrizione fisica |
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1 online resource (236 pages) |
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Collana |
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Texts and Readings in Mathematics, , 2366-8725 ; ; 84 |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Operator theory |
Functional analysis |
Geometry |
Operator Theory |
Functional Analysis |
Geometria |
Anàlisi funcional |
Teoria d'operadors |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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. |
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