Wold–Słociński decompositions for commuting isometric triples
Tudor Binzar , Zbigniew Burdak , Cristian Lazureanu , Dan Popovici , Marek Słociński
AbstractExtending 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.
|Journal series||Journal of Mathematical Analysis and Applications, ISSN 0022-247X, e-ISSN 1096-0813, (N/A 70 pkt)|
|Publication size in sheets||83|
|Keywords in English||Isometry, Unitary operator, Unilateral shift, Wold decomposition, Commuting isometric tuple, Słociński decomposition|
|Publication indicators||= 1; : 2018 = 1.187; : 2018 = 1.188 (2) - 2018=1.219 (5)|
|Citation count*||2 (2020-08-06)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.