國立虎尾科技大學 |

Dilations, completely positive maps and geometry

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Dilations, completely positive maps and geometry/ by 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

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:

1436256
Dilation theory (Operator theory)

LC Class. No.: QA329

Dewey Class. No.: 515.724

Dilations, completely positive maps and geometry
LDR:02586nam a2200337 a 4500 001 1120770
003 DE-He213
005 20240201214456.0
006 m d
007 cr nn 008maaau
008 240612s2023 si s 0 eng d
020 $a 9789819983520 $q (electronic bk.)
020 $a 9789819983513 $q (paper)
024 7 $a 10.1007/978-981-99-8352-0 $2 doi
035 $a 978-981-99-8352-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA329
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.724 $2 23
090 $a QA329 $b .B575 2023
100 1 $a Bhat, B. V. Rajarama. $3 1436255
245 1 0 $a Dilations, completely positive maps and geometry $h [electronic resource] / $c by B.V. Rajarama Bhat, Tirthankar Bhattacharyya.
260 $a Singapore : $c 2023. $b Springer Nature Singapore : $b Imprint: Springer,
300 $a xi, 229 p. : $b ill., digital ; $c 24 cm.
490 1 $a Texts and readings in mathematics, $x 2366-8725 ; $v 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.
650 0 $a Dilation theory (Operator theory) $3 1436256
650 0 $a Hilbert space. $3 580375
650 1 4 $a Operator Theory. $3 672127
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Geometry. $3 579899
700 1 $a Bhattacharyya, Tirthankar. $3 1069809
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Texts and readings in mathematics ; $v 37-38. $3 1052972
856 4 0 $u https://doi.org/10.1007/978-981-99-8352-0
950 $a Mathematics and Statistics (SpringerNature-11649)