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Dilations, completely positive maps and geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dilations, completely positive maps and geometryby B.V. Rajarama Bhat, Tirthankar Bhattacharyya.
Author:	Bhat, B. V. Rajarama.
other author:	Bhattacharyya, Tirthankar.
Published:	Singapore :Springer Nature Singapore :2023.
Description:	xi, 229 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Dilation theory (Operator theory)
Online resource:	https://doi.org/10.1007/978-981-99-8352-0
ISBN:	9789819983520$q(electronic bk.)

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 ;74..

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$q(electronic bk.)

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

965912
Dilation theory (Operator theory)

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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