Hilbert \(C^*\) and \(W^*\)-modules and their morphisms (Q1576010)

The paper is a survey on the theory of Hilbert \(C^\ast\)- and \(W^\ast\)-modules and its applications built on lectures given at the State Univ. of Moscow in 1996. In the first two sections the authors present the original work by W. L. Paschke on Hilbert \(C^\ast\)-modules, and the applications obtained by A. S. Mishchenko and A. T. Fomenko to the index theory of generalized Fredholm operators. In the next section they collect properties of Hilbert \(W^\ast\)-modules, in particular, the characterization of self-dual ones given by M. Frank. In the final section they study reflexive Hilbert \(W^\ast\)-modules, referring to work done by V. A. Trofimov and conclude with some of their own results on conditional expectations obtained in joint work with M. Frank.