On the Model and Invariant Subspaces for Pairs of Commuting Isometries
AbstractThe paper is devoted to a model and joint invariant subspaces under a pair of commuting isometries. A certain class of pairs of commuting isometries is defined. We give a model for such pairs and show that an arbitrary pair of commuting isometries has a minimal extension to a pair in the defined class. Subsequently we investigate a model for a general commuting pair of isometries via joint invariant subspaces of this extension. As an application operators of multiplication by independent variables on the Hardy space over the torus are extended to a pair in the defined class and joint invariant subspaces of the extension are described.
|Journal series||Integral Equations and Operator Theory, ISSN 0378-620X, e-ISSN 1420-8989, (N/A 100 pkt)|
|Publication size in sheets||1.1|
|Keywords in English||Invariant subspaces, Beurling theorem, Multiplication operator over bi-disk, Hardy space, Isometries|
|License||Journal (articles only); author's original; ; after publication|
|Publication indicators||= 0; : 2018 = 0.887; : 2018 = 0.652 (2) - 2018=0.775 (5)|
|Citation count*||1 (2020-08-10)|
|Finansowanie||This research was financed by the Ministry of Science and Higher Education of the Republic of Poland.|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.