Analytic Hilbert Modules

TL;DR: The seminal 1989 work of Douglas and Paulsen in the theory of analytic Hilbert modules precipitated a number of major research efforts as discussed by the authors, which led to some intriguing and valuable results, particularly in the areas of operator theory and functional analysis.

Abstract: The seminal 1989 work of Douglas and Paulsen in the theory of analytic Hilbert modules precipitated a number of major research efforts. This in turn led to some intriguing and valuable results, particularly in the areas of operator theory and functional analysis. With the field now beginning to blossom, the time has come to collect those results under one cover. Written by two of the most active and often-cited researchers in the field, Analytic Hilbert Modules reports on the progress made by the authors and others, including the characteristic space theory, rigidity, the equivalence problem, the Arveson modules, extension theory, and reproducing Hilbert spaces on n-dimensional complex space.