Titlebook: Algebraic Methods in Operator Theory; Raúl E. Curto,Palle E. T. J?rgensen Conference proceedings 1994 Springer Science+Business Media New

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The Local de Branges-Rovnyak Construction and Complete Nevanlinna-Pick Kernelsnted. This construction generalizes versions of the de Branges-Rovnyak construction [7] used by a number of authors, including Agler [5] and Muller [9] for weighted shifts (diagonal kernels) satisfying various polynomial identities.

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Operator-Valued Poisson Kernels and Standard Models in Several Variablestrum of .. Let . ? ? be the open unit disc. If . ∈ .(.) is such that σ(.) ? ., then for each analytic polynomial . (more generally, for each . holomorphic in . and continuous on .we have (see [Vas]) .where σ is the normalized Lebesgue measure on ?.. If, moreover,∥.∥ ≤ 1, then.is positive for all . ∈

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On Banach Algebras Generated by Two Idempotentsal algebras, the Gel’fand map realizes an imbedding into the algebra of all continuous functions on a well-defined set, namely the space of maximal ideals. Analogously, a semisimple algebra can be shown to be isomorphic to a subalgebra of all continuous 2 x 2 matrix-valued functions on a compact set