Wold–Słociński decompositions for commuting isometric triples

Tudor Binzar , Zbigniew Burdak , Cristian Lazureanu , Dan Popovici , Marek Słociński


Extending two remarkable results by von Neumann–Halmos–Wold (for isometric operators) and Słociński (for pairs of commuting isometries) we discuss the possibility to decompose a given commuting triple of isometric operators, acting on a Hilbert space , into the direct sum between commuting triples consisting of unitary operators and/or unilateral shifts. We prove that such a decomposition exists if and only if the pairs , and have decompositions of Wold–Słociński type. If only two of these pairs are supposed to have such a decomposition then the Wold–Słociński decomposition associated to V has seven summands. Several structure results, of geometric type, for these summands are also presented. Examples and counterexamples are used for illustrative purposes. Certain results are presented in full generality, i.e., for commuting isometric n-tuples.
Author Tudor Binzar
Tudor Binzar,,
, Zbigniew Burdak (FoEEaLS / DoAM)
Zbigniew Burdak,,
- Department of Applied Mathematics
, Cristian Lazureanu
Cristian Lazureanu,,
, Dan Popovici
Dan Popovici,,
, Marek Słociński
Marek Słociński,,
Journal seriesJournal of Mathematical Analysis and Applications, ISSN 0022-247X, e-ISSN 1096-0813, (N/A 70 pkt)
Issue year2019
Publication size in sheets83
Keywords in EnglishIsometry, Unitary operator, Unilateral shift, Wold decomposition, Commuting isometric tuple, Słociński decomposition
ASJC Classification2603 Analysis; 2604 Applied Mathematics
Internal identifierWIŚIG/2019/38
Languageen angielski
Score (nominal)70
Score sourcejournalList
Publication indicators WoS Citations = 1; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 1.187; WoS Impact Factor: 2018 = 1.188 (2) - 2018=1.219 (5)
Citation count*2 (2020-08-06)
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