Banach Journal of Mathematical Analysis

Szegö-type decompositions for isometries

Zbigniew Burdak, Marek Kosiek, Patryk Pagacz, and Marek Słociński

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The notion of Szegö-type properties of positive Borel measures is well known and widely exploited. In this paper, we consider a class of orthogonal decompositions of isometries on Hilbert spaces which correspond to Szegö-type properties of their elementary measures. Our decompositions are closely connected with some special families of invariant subspaces. It is shown that this connection holds for the decomposition constructed in the paper. We illustrate our results with several examples. We also give a short proof of Mlak’s theorem on the elementary measures of completely nonunitary contractions.

Article information

Banach J. Math. Anal., Volume 10, Number 3 (2016), 593-607.

Received: 16 April 2015
Accepted: 19 November 2015
First available in Project Euclid: 22 July 2016

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Zentralblatt MATH identifier

Primary: 47B20: Subnormal operators, hyponormal operators, etc.
Secondary: 47B40: Spectral operators, decomposable operators, well-bounded operators, etc. 47A20: Dilations, extensions, compressions 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

isometries Szegö measures Wold decomposition wandering vectors invariant subspaces


Burdak, Zbigniew; Kosiek, Marek; Pagacz, Patryk; Słociński, Marek. Szegö-type decompositions for isometries. Banach J. Math. Anal. 10 (2016), no. 3, 593--607. doi:10.1215/17358787-3607420.

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