The Arveson Extension Theorem and coanalytic models
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- Agler, J. Integr equ oper theory (1982) 5: 608. doi:10.1007/BF01694057
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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.