Abstract: The notion of a Hilbert C*-module is a generalization of the notion of a Hilbert space. The first use of such objects was made by I. Kaplansky. The research on Hilbert C*-modules began in the 70’s in the work of the induced representations of C*-algebras by M. A. Rieffel and the doctoral dissertation of W. L. Paschke. It is also used to study Morita equivalence of C*-algebras, KK-theory of C*-algebras, operator K-theory, C*-algebra quantum group and theory of operator spaces. In this lecture series, I would like to revisit the theory of Hilbert C*-module and discuss some of its recent exciting applications.


The following links are the video recordings and slides of this lecture series.

Lecture I Lecture II Lecture III Lecture IV

Slides I Slides II