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- W2904387526 abstract "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 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 ( V 1 V 2 , V 3 ) , ( V 2 V 3 , V 1 ) and ( V 1 V 3 , V 2 ) 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." @default.
- W2904387526 created "2018-12-22" @default.
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- W2904387526 date "2019-04-01" @default.
- W2904387526 modified "2023-09-28" @default.
- W2904387526 title "Wold–Słociński decompositions for commuting isometric triples" @default.
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- W2904387526 doi "https://doi.org/10.1016/j.jmaa.2018.12.016" @default.
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