03700nam 22006855 450 991083100220332120260211152536.09789819983520981998352510.1007/978-981-99-8352-0(MiAaPQ)EBC31102394(Au-PeEL)EBL31102394(DE-He213)978-981-99-8352-0(CKB)30181657400041(OCoLC)1420629886(EXLCZ)993018165740004120240201d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierDilations, Completely Positive Maps and Geometry /by B.V. Rajarama Bhat, Tirthankar Bhattacharyya1st ed. 2023.Singapore :Springer Nature Singapore :Imprint: Springer,2023.1 online resource (236 pages)Texts and Readings in Mathematics,2366-8725 ;84Print version: Bhat, B. V. Rajarama Dilations, Completely Positive Maps and Geometry Singapore : Springer Singapore Pte. Limited,c2024 9789819983513 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.Texts and Readings in Mathematics,2366-8725 ;84Operator theoryFunctional analysisGeometryOperator TheoryFunctional AnalysisGeometryGeometriathubAnàlisi funcionalthubTeoria d'operadorsthubLlibres electrònicsthubOperator theory.Functional analysis.Geometry.Operator Theory.Functional Analysis.Geometry.GeometriaAnàlisi funcionalTeoria d'operadors515.724Bhat B. V. Rajarama1680034Bhattacharyya Tirthankar1680035MiAaPQMiAaPQMiAaPQBOOK9910831002203321Dilations, Completely Positive Maps and Geometry4048690UNINA