Michael Dritschel

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Agler's abstract model theory is applied to C, the family of operators with unitary-dilations, where is a xed number in (0; 2]. The extremals, which are the collection of operators in C with the property that the only extensions of them which remain in the family are direct sums, are characterized in a variety of manners. They form a part of any model, and(More)
Let R denote a domain in C with boundary B. Let X denote the closure of R. An operator T on a complex Hilbert space H has X as a spectral set if σ(T ) ⊂ X and ‖f(T )‖ ≤ ‖f‖R = sup{|f(z)| : z ∈ R} for every rational function f with poles off X. The expression f(T ) may be interpreted either in terms of the Riesz functional calculus, or simply by writing the(More)
A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a family of test functions over a broad class of semigroupoids. There is then an associated interpolation theorem.(More)
The Fejér-Riesz theorem has inspired numerous generalizations in one and several variables, and for matrixand operator-valued functions. This paper is a survey of some old and recent topics that center around Rosenblum’s operator generalization of the classical Fejér-Riesz theorem. Mathematics Subject Classification (2000). Primary 47A68; Secondary 60G25,(More)