Article

Integral Equations and Operator Theory

, Volume 5, Issue 1, pp 608-631

The Arveson Extension Theorem and coanalytic models

  • Jim AglerAffiliated withDepartment of Mathematics, University of Virginia

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Abstract

We develop techniques which allow one to describe in simple terms the set of operators on Hilbert space of the form M* (∞) |M, where M is multiplication by z on a Hilbert space of analytic functions satisfying certain technical assumptions, M* (∞) is the direct sum of a countably infinite number of copies of M*, andM is invariant for M* (∞). One of the main ingredients in our technique is the Arveson Extension Theorem and this paper illustrates the great power and tractability of that theorem in a concrete setting.