Dilations,completely positive maps and geometry
Material type: TextLanguage: English Series: . 84 | Texts and Readings in Mathematics ; 84Publication details: New Delhi: Hindustan Book Agency, 2023. Description: xi, 246p. HbkISBN: 9788195782925Subject(s): GeometryDDC classification: 514Item type | Current library | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|
NBHM Books | SMS Library | 514 BHA-D (Browse shelf(Opens below)) | Available | N369 |
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512.8:511.384 HAL-L Lie groups, lie algebras and representations:an elementary introduction | 514 AKB-G Geometry ,Algebra , Number theory and their information Technology Application | 514 BAL-F Finite geometry and combinatorial applications | 514 BHA-D Dilations,completely positive maps and geometry | 514 BLO-F Finite geometries | 514 BLO-F Finite geometries | 514 BRA-G Geometry |
Includes bibliography and index.
http://www.hindbook.com/images/CONTENTS.pdf
This book deals with dilation theory of operators on Hilbert spaces and its relationship to complex geometry. Classical as well as very modern topics are covered. 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 deals with various geometrical objects like the bidisc, the Euclidean unit ball and the symmetrized bidisc. It shows the similarities and the differences between dilation theory in these domains. While completely positive maps play a big role in 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. Thus, the book will introduce the reader to different techniques applicable in different domains.
The first three chapters are suitable for an advanced course in operator theory in the final year of M.Sc. The whole book can be used for a first-year course for Ph.D. students. Portions of the book could also serve as material for advanced training schools in mathematics. After a course based on this book, students will be ready to work on state-of-the-art problems of research in operator theory.
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