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Abstract: In this note we study the completely non unitary contractions on separablecomplex Hilbert spaces which have polynomial characteristic functions. Theseoperators are precisely those which admit a matrix representation of the formT = S and * and * 0 and N and * 0and 0and C, where $S$ and C^* are unilateral shifts ofarbitrary multiplicities and $N$ is nilpotent. We prove that dimension of kerS^* and dimension of ker C are unitary invariants of $T$ and that N, up to aquasi-similarity is uniquely determined by T. Also, we give a completeclassification of the subclass of those contractions for which theircharacteristic functions are monomials.



Autor: Ciprian Foias, Jaydeb Sarkar

Fuente: https://arxiv.org/



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