Michael Dritschel

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For R a bounded triply connected domain with boundary consisting of disjoint Jordan loops there exists an operator T on a complex Hilbert space H so that the closure of R is a spectral set for T , but T does not dilate to a normal operator with spectrum in B, the boundary of R. There is considerable overlap with the construction of an example on such a(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)