Publisher's Synopsis
This Research Note presents a new approach to the application of algebraic language of modules to the study of bounded operators on Hilbert space. Areas which the authors discuss include the following - how a single operator makes the Hilbert space into a module over the ring of polynomials in one variable; the canonical model theory for contraction operators; and multi-variate operator theory as Hilbert modules over multi-variate rings. In their study of the subject, the authors use techniques and concepts from both algebraic and differential geometry.;The book concludes with a look ahead to the likely lines of development of recent results in the subject. It attempts to encourage researchers to adopt this new point of view towards operator theory.;It is aimed at graduate students and researchers working in the area of functional analysis or operator theory.
