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Dilations, completely positive maps and geometry

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Dilations, completely positive maps and geometry/ by B.V. Rajarama Bhat, Tirthankar Bhattacharyya.
作者:	Bhat, B. V. Rajarama.
其他作者:	Bhattacharyya, Tirthankar.
出版者:	Singapore :Springer Nature Singapore : : 2023.,
面頁冊數:	xi, 229 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Geometry. -
電子資源:	https://doi.org/10.1007/978-981-99-8352-0
ISBN:	9789819983520

Dilations, completely positive maps and geometry
Bhat, B. V. Rajarama.

Dilations, completely positive maps and geometry[electronic resource] /by B.V. Rajarama Bhat, Tirthankar Bhattacharyya. - Singapore :Springer Nature Singapore :2023. - xi, 229 p. :ill., digital ;24 cm. - Texts and readings in mathematics,v. 842366-8725 ;. - Texts and readings in mathematics ;37-38..

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.

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.

ISBN: 9789819983520

Standard No.: 10.1007/978-981-99-8352-0doiSubjects--Topical Terms:

579899
Geometry.

LC Class. No.: QA329

Dewey Class. No.: 515.724

Dilations, completely positive maps and geometry
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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.
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