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Decompositions and asymptotic limit for bicontractions

Marek Kosiek, Laurian Suciu (2012)

Annales Polonici Mathematici

The asymptotic limit of a bicontraction T (that is, a pair of commuting contractions) on a Hilbert space is used to describe a Nagy-Foiaş-Langer type decomposition of T. This decomposition is refined in the case when the asymptotic limit of T is an orthogonal projection. The case of a bicontraction T consisting of hyponormal (even quasinormal) contractions is also considered, where we have S T * = S ² T * .

Once more about the monotonicity of the Temple quotients

Drahoslava Janovská, Ivo Marek (1984)

Aplikace matematiky

A new proof of the monotonicity of the Temple quotients for the computation of the dominant eigenvalue of a bounded linear normal operator in a Hilbert space is given. Another goal of the paper is a precise analysis of the length of the interval for admissible shifts for the Temple quotients.

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