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On th roots of bounded and unbounded quasinormal operators

2023
journal article
article
10.1007/s10231-022-01281-z
Journal
Annali di Matematica Pura ed Applicata
100
Author
Pietrzycki Paweł

Stochel Jan
Volume
202
Pages
1313-1333
ISSN
0373-3114
eISSN
1618-1891
Keywords in English

quasinormal operator

subnormal operator

class A operator

intertwining theorem

stieltjes moment problem

URL
https://link.springer.com/article/10.1007/s10231-022-01281-z
Access date
2024-03-29
Language
English
Journal language
English
Abstract in English

In a recent paper (JFA 278:108342, 2020), R. E. Curto, S. H. Lee and J. Yoon asked the following question: Let T be a subnormal operator, and assume that T2 is quasinormal. Does it follow that T is quasinormal? In (JFA 280:109001, 2021) we answered this question in the affirmative. In the present paper, we will extend this result in two directions. Namely, we prove that hyponormal (or even much beyond this class) nth roots of bounded quasinormal operators are quasinormal. On the other hand, we show that subnormal nth roots of unbounded quasinormal operators are quasinormal. We also prove that a non-normal quasinormal operator having a quasinormal nth root has a non-quasinormal nth root.

Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
Scopus© citations
4
dc.abstract.enIn a recent paper (JFA 278:108342, 2020), R. E. Curto, S. H. Lee and J. Yoon asked the following question: Let T be a subnormal operator, and assume that T2 is quasinormal. Does it follow that T is quasinormal? In (JFA 280:109001, 2021) we answered this question in the affirmative. In the present paper, we will extend this result in two directions. Namely, we prove that hyponormal (or even much beyond this class) nth roots of bounded quasinormal operators are quasinormal. On the other hand, we show that subnormal nth roots of unbounded quasinormal operators are quasinormal. We also prove that a non-normal quasinormal operator having a quasinormal nth root has a non-quasinormal nth root.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Matematykipl
dc.contributor.authorPietrzycki, Paweł - 164544 pl
dc.contributor.authorStochel, Jan - 132109 pl
dc.date.accession2024-03-29pl
dc.date.accessioned2023-05-31T15:48:59Z
dc.date.available2023-05-31T15:48:59Z
dc.date.issued2023pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.physical1313-1333pl
dc.description.versionostateczna wersja wydawcy
dc.description.volume202pl
dc.identifier.doi10.1007/s10231-022-01281-zpl
dc.identifier.eissn1618-1891pl
dc.identifier.issn0373-3114pl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/311891
dc.identifier.weblinkhttps://link.springer.com/article/10.1007/s10231-022-01281-zpl
dc.languageengpl
dc.language.containerengpl
dc.rightsUdzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa*
dc.rights.licenceCC-BY
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/legalcode.pl*
dc.share.typeinne
dc.subject.enquasinormal operatorpl
dc.subject.ensubnormal operatorpl
dc.subject.enclass A operatorpl
dc.subject.enintertwining theorempl
dc.subject.enstieltjes moment problempl
dc.subtypeArticlepl
dc.titleOn $n$th roots of bounded and unbounded quasinormal operatorspl
dc.title.journalAnnali di Matematica Pura ed Applicatapl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
In a recent paper (JFA 278:108342, 2020), R. E. Curto, S. H. Lee and J. Yoon asked the following question: Let T be a subnormal operator, and assume that T2 is quasinormal. Does it follow that T is quasinormal? In (JFA 280:109001, 2021) we answered this question in the affirmative. In the present paper, we will extend this result in two directions. Namely, we prove that hyponormal (or even much beyond this class) nth roots of bounded quasinormal operators are quasinormal. On the other hand, we show that subnormal nth roots of unbounded quasinormal operators are quasinormal. We also prove that a non-normal quasinormal operator having a quasinormal nth root has a non-quasinormal nth root.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorpl
Pietrzycki, Paweł - 164544
dc.contributor.authorpl
Stochel, Jan - 132109
dc.date.accessionpl
2024-03-29
dc.date.accessioned
2023-05-31T15:48:59Z
dc.date.available
2023-05-31T15:48:59Z
dc.date.issuedpl
2023
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.physicalpl
1313-1333
dc.description.version
ostateczna wersja wydawcy
dc.description.volumepl
202
dc.identifier.doipl
10.1007/s10231-022-01281-z
dc.identifier.eissnpl
1618-1891
dc.identifier.issnpl
0373-3114
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/311891
dc.identifier.weblinkpl
https://link.springer.com/article/10.1007/s10231-022-01281-z
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licence
CC-BY
dc.rights.uri*
http://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.type
inne
dc.subject.enpl
quasinormal operator
dc.subject.enpl
subnormal operator
dc.subject.enpl
class A operator
dc.subject.enpl
intertwining theorem
dc.subject.enpl
stieltjes moment problem
dc.subtypepl
Article
dc.titlepl
On $n$th roots of bounded and unbounded quasinormal operators
dc.title.journalpl
Annali di Matematica Pura ed Applicata
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations
Wydział Matematyki i Informatyki
Pietrzycki, Paweł
Stochel, Jan

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