On the Model and Invariant Subspaces for Pairs of Commuting Isometries

Zbigniew Burdak

Abstract

The 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.
Author Zbigniew Burdak (FoEEaLS / DoAM)
Zbigniew Burdak,,
- Department of Applied Mathematics
Journal seriesIntegral Equations and Operator Theory, ISSN 0378-620X, e-ISSN 1420-8989, (N/A 100 pkt)
Issue year2019
Vol91
No3
Pages1-23
Publication size in sheets1.1
Article number22
Keywords in EnglishInvariant subspaces, Beurling theorem, Multiplication operator over bi-disk, Hardy space, Isometries
ASJC Classification2602 Algebra and Number Theory; 2603 Analysis
DOIDOI:10.1007/s00020-019-2516-4
URL https://link.springer.com/content/pdf/10.1007%2Fs00020-019-2516-4.pdf
Internal identifierWIŚIG/2019/53
Languageen angielski
LicenseJournal (articles only); author's original; Uznanie Autorstwa (CC-BY); after publication
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On the Model and Invariant Subspaces for Pairs of Commuting Isometries of 30-09-2019
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Score (nominal)100
Score sourcejournalList
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.887; WoS Impact Factor: 2018 = 0.652 (2) - 2018=0.775 (5)
Citation count*1 (2020-04-08)
Additional fields
FinansowanieThis research was financed by the Ministry of Science and Higher Education of the Republic of Poland.
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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