Abstract
In [3] we set forth a program for placing the study of Hilbert space operators in the context of Hilbert modules over function algebras. One of the goals of this formulation is to suggest both new questions and new machinery for answering them based on the well developed analogous theories for modules in algebraic and analytic geometry. It is hoped, moreover, that the transition from the theory of one to that of several operators will be facilitated in this framework much as happens in algebra. We should add, however, that we do not expect that progress will be easy or that the techniques from algebra will apply without considerable adaptation and work — only that the general approach will be useful.
Research partially supported by a grant from the National Science Foundation.
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References
Abrahamse, M.B.; Douglas, R.G.: A class of subnormal operators related to multiply-connected domains, Adv. Math. 19(1976), 106–148.
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Douglas, R.G.: Hilbert modules over function algebras, in Advances in invariant subspaces and other results of operator theory, Birkhauser Verlag, Basel, 1986, pp. 125–139.
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Sz.-Nagy, B.; Foiaş, C.: Harmonic analysis of operators on Hilbert space, American Elsevier, New York, 1970.
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© 1988 Birkhäuser Verlag Basel
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Douglas, R.G. (1988). On Šilov Resolution of Hilbert Modules. In: Arsene, G. (eds) Special Classes of Linear Operators and Other Topics. Operator Theory: Advances and Applications, vol 28. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9164-6_4
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DOI: https://doi.org/10.1007/978-3-0348-9164-6_4
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-1970-0
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