000			01776nam a22002057a 4500
008			240207b |||||||| |||| 00| 0 eng d
020			_a9788195782925 (HB)
041			_aeng
080			_a515.1 _bBHA
100			_aBhat, Rajarama B.V.
245			_aDilations, completely positive maps and geometry
260			_aNew Delhi _bHindustan Book Agency _c2023
300			_axi, 248p
490			_aTexts and Readings in Mathematics _v84
500			_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.
650			_aDilation theory _vComplex geometry
690			_aMathematics
700			_aBhattacharyya, Tirthankar
942			_cBK
999			_c60028 _d60028