Hilbert Cmodules Vladimir Markovich Manulov Evgeni Vadimovich Troitski by Vladimir Markovich Manuǐlov, Evgeniĭ Vadimovich Troit︠s︡kiĭ 9780821838105, 0821838105 instant download after payment.

Based on lectures delivered by the authors at Moscow State University, this volume presents a detailed introduction to the theory of Hilbert $C^*$-modules. Hilbert $C^*$-modules provide a natural generalization of Hilbert spaces arising when the field of scalars $\mathbf{C}$ is replaced by an arbitrary $C^*$-algebra. The general theory of Hilbert $C^*$-modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool in operator algebras theory, index theory of elliptic operators, $K$- and $KK$-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert $C^*$-modules is interesting on its own. In this book, the authors explain in detail the basic notions and results of the theory, and provide a number of important examples. Some results related to the authors' research interests are also included. A large part of the book is devoted to structural results (self-duality, reflexivity) and to nonadjointable operators. Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.