Wold-Slocinski decompositions for commuting isometric triples

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Binzar, Tudor¹  Burdak, Zbigniew²  Lazureanu, Cristian¹  Popovici, Dan³  Slocinski, Marek⁴ 

[1] Politehn Univ Timisoara, Dept Math, Piata Victoriei 2, Timisoara 300006, Romania

[2] Univ Agr, Inst Math, Ul Balicka 253c, PL-30198 Krakow, Poland

[3] West Univ Timisoara, Dept Math, Bd V Parvan 4, Timisoara 300223, Romania

[4] Uniwersytet Jagiellonski, Wydzial Matemat & Informatyki, Ul Prof St Lojasiewicza 6, PL-30348 Krakow, Poland

关键词: Isometry;    Unitary operator;    Unilateral shift;    Wold decomposition;    Commuting isometric tuple;    Slocinski decomposition;   

DOI  :  10.1016/j.jmaa.2018.12.016

来源: Elsevier

【 摘 要 】

Extending two remarkable results by von Neumann-Halmos-Wold (for isometric operators) and Slocinski (for pairs of commuting isometries) we discuss the possibility to decompose a given commuting triple V = (V-1, V-2, V-3) of isometric operators, acting on a Hilbert space H, 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 (V1V2, V-3), (V2V3, V-1) and (V1V3, V-2) have decompositions of Wold Slocinski type. If only two of these pairs are supposed to have such a decomposition then the Wold Slocinski 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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