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The Taylor spectrum of pairs of isometries

2026
journal article
article
10.1007/s00020-026-02859-5
Journal
Integral Equations and Operator Theory
100
Author
Burdak Zbigniew

Pagacz Patryk
Volume
98
Number
3
Article ID
34
ISSN
0378-620X
eISSN
1420-8989
URL
https://link.springer.com/article/10.1007/s00020-026-02859-5#article-info
Access date
2026-08-26
Language
English
Journal language
English
Abstract in English

In the paper we fully describe the Taylor spectrum of pairs of isometries defined by diagrams. In most cases both isometries in such pairs have nontrivial shift part, and its Taylor spectrum is a proper sub- set (of Lebesgue measure in (0, π2)) of the closed bidisk. In particular, there are pairs of isometries which spectrum is equal to {(μ, λ) ∈ D2 : |μ|a ≤ |λ| ≤ |μ|b} for any 0 < a ≤ b < ∞.

Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.abstract.enIn the paper we fully describe the Taylor spectrum of pairs of isometries defined by diagrams. In most cases both isometries in such pairs have nontrivial shift part, and its Taylor spectrum is a proper sub- set (of Lebesgue measure in (0, π2)) of the closed bidisk. In particular, there are pairs of isometries which spectrum is equal to {(μ, λ) ∈ D2 : |μ|a ≤ |λ| ≤ |μ|b} for any 0 < a ≤ b < ∞.
dc.affiliationWydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorBurdak, Zbigniew
dc.contributor.authorPagacz, Patryk - 106982
dc.date.accession2026-08-26
dc.date.accessioned2026-08-27T06:59:52Z
dc.date.available2026-08-27T06:59:52Z
dc.date.createdat2026-08-24T09:36:16Zen
dc.date.issued2026
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.number3
dc.description.versionostateczna wersja wydawcy
dc.description.volume98
dc.identifier.articleid34
dc.identifier.doi10.1007/s00020-026-02859-5
dc.identifier.eissn1420-8989
dc.identifier.issn0378-620X
dc.identifier.projectDRC AI
dc.identifier.urihttps://ruj.uj.edu.pl/handle/item/581154
dc.identifier.weblinkhttps://link.springer.com/article/10.1007/s00020-026-02859-5#article-info
dc.languageeng
dc.language.containereng
dc.rightsUdzielam licencji. Uznanie autorstwa - Użycie niekomercyjne - Bez utworów zależnych 4.0 Międzynarodowa
dc.rights.licenceCC-BY-NC-ND
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.pl
dc.share.typeinne
dc.source.integratorfalse
dc.subtypeArticle
dc.titleThe Taylor spectrum of pairs of isometries
dc.title.journalIntegral Equations and Operator Theory
dc.typeJournalArticle
dspace.entity.typePublicationen
dc.abstract.en
In the paper we fully describe the Taylor spectrum of pairs of isometries defined by diagrams. In most cases both isometries in such pairs have nontrivial shift part, and its Taylor spectrum is a proper sub- set (of Lebesgue measure in (0, π2)) of the closed bidisk. In particular, there are pairs of isometries which spectrum is equal to {(μ, λ) ∈ D2 : |μ|a ≤ |λ| ≤ |μ|b} for any 0 < a ≤ b < ∞.
dc.affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.author
Burdak, Zbigniew
dc.contributor.author
Pagacz, Patryk - 106982
dc.date.accession
2026-08-26
dc.date.accessioned
2026-08-27T06:59:52Z
dc.date.available
2026-08-27T06:59:52Z
dc.date.createdaten
2026-08-24T09:36:16Z
dc.date.issued
2026
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.number
3
dc.description.version
ostateczna wersja wydawcy
dc.description.volume
98
dc.identifier.articleid
34
dc.identifier.doi
10.1007/s00020-026-02859-5
dc.identifier.eissn
1420-8989
dc.identifier.issn
0378-620X
dc.identifier.project
DRC AI
dc.identifier.uri
https://ruj.uj.edu.pl/handle/item/581154
dc.identifier.weblink
https://link.springer.com/article/10.1007/s00020-026-02859-5#article-info
dc.language
eng
dc.language.container
eng
dc.rights
Udzielam licencji. Uznanie autorstwa - Użycie niekomercyjne - Bez utworów zależnych 4.0 Międzynarodowa
dc.rights.licence
CC-BY-NC-ND
dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.pl
dc.share.type
inne
dc.source.integrator
false
dc.subtype
Article
dc.title
The Taylor spectrum of pairs of isometries
dc.title.journal
Integral Equations and Operator Theory
dc.type
JournalArticle
dspace.entity.typeen
Publication
Affiliations
No affiliation
Burdak, Zbigniew
Wydział Matematyki i Informatyki
Pagacz, Patryk
mathematics

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