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July 2016 Szegö-type decompositions for isometries
Zbigniew Burdak, Marek Kosiek, Patryk Pagacz, Marek Słociński
Banach J. Math. Anal. 10(3): 593-607 (July 2016). DOI: 10.1215/17358787-3607420


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.


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Zbigniew Burdak. Marek Kosiek. Patryk Pagacz. Marek Słociński. "Szegö-type decompositions for isometries." Banach J. Math. Anal. 10 (3) 593 - 607, July 2016.


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

zbMATH: 06621471
MathSciNet: MR3528349
Digital Object Identifier: 10.1215/17358787-3607420

Primary: 47B20
Secondary: 47A20, 47B37, 47B40

Rights: Copyright © 2016 Tusi Mathematical Research Group


Vol.10 • No. 3 • July 2016
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