Mathematical Sciences: Multivariable Operator Theory

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9401455 Curto The research of Curto will involve five projects from the subject of multivariable operator theory. These projects are the following: 1.A description of the spectral picture of multiplication on functional Hilbert spaces over Reinhardt and matrix Reinhardt domains. 2.Further characterizations of polynomial hyponormal operators. 3.Using hyponormal operator techniques to characterize initial segments of moment sequences. 4.A search for an Sz. Nagy-Foias dilation theory in several variables. 5.Understand the relationship between Taylor spectrum and other spectral systems using topological and K-theoretic invariants. Hilbert space operators are infinite generalizations of matrices. The infinite generalization of a vector is frequently a function and for this reason Hilbert space operators are frequently modeled as the operator of multiplication on a space of functions. This project involves finding such models for operators or tuples of operators. Once such models are obtained many basic questions about the structure of these operators become more natural. ***