Hilbert Module approach to operator theory I

We will begin by briefly describing some of the reasons to be interested in Hilbert module approach to operator theory. Then we will review some recent results and developments in function theory and (multivariable) operator theory. Along the way, we will discuss a list of examples and (wild) conjectures. The first talk will focus on: classical Sz.-Nagy and Foias dilation theory, von Neumann inequality, Beurling-Lax-Halmos theorem, submodules, quotient modules along with a quick introduction of reproducing kernel Hilbert spaces.