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: | 9789819983544 |
| Publication date: | 2nd February 2025 |
| Author: | B V Rajarama Bhat, Tirthankar Bhattacharyya |
| Publisher: | Springer an imprint of Springer Nature Singapore |
| Format: | Paperback |
| Pagination: | 229 pages |
| Series: | Texts and Readings in Mathematics |
| Genres: |
Functional analysis and transforms 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 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.
Dilations, Completely Positive Maps and Geometry features in the following genres: Functional analysis and transforms, Geometry
Dilations, Completely Positive Maps and Geometry is available in Paperback, Hardback
Dilations, Completely Positive Maps and Geometry was written by B V Rajarama Bhat, Tirthankar Bhattacharyya and published by Springer an imprint of Springer Nature Singapore
Dilations, Completely Positive Maps and Geometry has 229 pages
Yes it is part of Texts and Readings in Mathematics series
£98.99