Items related to Hilbert Modules over Function Algebras (Research Notes...
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.
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