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All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C-envelope.

- Michael Dritschel, Philip Protter
- Finance and Stochastics
- 1999

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)

The notion of a unitary realization is used to estimate derivatives of arbitrary order of functions in the Schur-Agler class on the polydisk and unit ball.

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)

- MICHAEL A. DRITSCHEL, STEFANIA MARCANTOGNINI
- 2008

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)

A multivariate version of Rosenblum’s Fejér-Riesz theorem on outer factorization of trigonometric polynomials with operator coefficients is considered. Due to a simplification of the proof of the single variable case, new necessary and sufficient conditions for the multivariable outer factorization problem are formulated and proved.

- Michael Dritschel, Daniel Estevez, Dmitry Yakubovich
- J. London Math. Society
- 2017

Jim Agler revolutionized the area of Pick interpolation with his realization theorem for what is now called the Agler-Schur class for the unit ball in C. We discuss an extension of these results to algebras of functions arising from test functions and the dual notion of a family of reproducing kernels, as well as the related interpolation theorem. When… (More)