LEADER 03700nam 22006855 450 001 9910831002203321 005 20260211152536.0 010 $a9789819983520 010 $a9819983525 024 7 $a10.1007/978-981-99-8352-0 035 $a(MiAaPQ)EBC31102394 035 $a(Au-PeEL)EBL31102394 035 $a(DE-He213)978-981-99-8352-0 035 $a(CKB)30181657400041 035 $a(OCoLC)1420629886 035 $a(EXLCZ)9930181657400041 100 $a20240201d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDilations, Completely Positive Maps and Geometry /$fby B.V. Rajarama Bhat, Tirthankar Bhattacharyya 205 $a1st ed. 2023. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2023. 215 $a1 online resource (236 pages) 225 1 $aTexts and Readings in Mathematics,$x2366-8725 ;$v84 311 08$aPrint version: Bhat, B. V. Rajarama Dilations, Completely Positive Maps and Geometry Singapore : Springer Singapore Pte. Limited,c2024 9789819983513 327 $aDilation 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. 330 $aThis book introduces the dilation theory of operators on Hilbert spaces and its relationship to complex geometry. Classical as well as very modern topics are covered in the book. On the one hand, it introduces the reader to the characteristic function, a classical object used by Sz.-Nagy and Foias and still a topic of current research. On the other hand, it describes the dilation theory of the symmetrized bidisc which has been developed mostly in the present century and is a very active topic of research. It also describes an abstract theory of dilation in the setting of set theory. This was developed very recently. A good portion of the book discusses various geometrical objects like the bidisc, the Euclidean unit ball, and the symmetrized bidisc. It shows the similarities and differences between the dilation theory in these domains. While completely positive maps play a big role in the dilation theory of the Euclidean unit ball, this is not so in the symmetrized bidisc for example. There, the central role is played by an operator equation. Targeted to graduate students and researchers, the book introduces the reader to different techniques applicable in different domains. 410 0$aTexts and Readings in Mathematics,$x2366-8725 ;$v84 606 $aOperator theory 606 $aFunctional analysis 606 $aGeometry 606 $aOperator Theory 606 $aFunctional Analysis 606 $aGeometry 606 $aGeometria$2thub 606 $aAnàlisi funcional$2thub 606 $aTeoria d'operadors$2thub 608 $aLlibres electrònics$2thub 615 0$aOperator theory. 615 0$aFunctional analysis. 615 0$aGeometry. 615 14$aOperator Theory. 615 24$aFunctional Analysis. 615 24$aGeometry. 615 7$aGeometria 615 7$aAnàlisi funcional 615 7$aTeoria d'operadors 676 $a515.724 700 $aBhat$b B. V. Rajarama$01680034 701 $aBhattacharyya$b Tirthankar$01680035 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910831002203321 996 $aDilations, Completely Positive Maps and Geometry$94048690 997 $aUNINA