A generalization of Banach’s lemma and its applications to perturbations of bounded linear operators

Let X be a Banach space and let P : X → X be a bounded linear operator. Using an algebraic inequality on the spectrum of P , we give a new sufficient condition that guarantees the existence of ( I – P ) −1 as a bounded linear operator on X , and a bound on its spectral radius is also obtained. This...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Applied Mathematics-A Journal of Chinese Universities 2024-06, Vol.39 (2), p.363-369
Hauptverfasser:	Wang, Zi, Ding, Jiu, Wang, Yu-wen
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Banach spaces Linear operators Mathematics Mathematics and Statistics Operators (mathematics) Perturbation methods
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	369
container_issue	2
container_start_page	363
container_title	Applied Mathematics-A Journal of Chinese Universities
container_volume	39
creator	Wang, Zi Ding, Jiu Wang, Yu-wen
description	Let X be a Banach space and let P : X → X be a bounded linear operator. Using an algebraic inequality on the spectrum of P , we give a new sufficient condition that guarantees the existence of ( I – P ) −1 as a bounded linear operator on X , and a bound on its spectral radius is also obtained. This generalizes the classic Banach lemma. We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.
doi_str_mv	10.1007/s11766-024-4872-3
format	Article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3066865132</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3066865132</sourcerecordid><originalsourceid>FETCH-LOGICAL-c268t-d2b22c2c0a6da52bd4292360c22e136112ec2787dd2d1599947746f9568641783</originalsourceid><addsrcrecordid>eNp1kMtOwzAQRS0EEhX0A9hZYh2wx69kWSpeUiU2sLZc2ymp0jjYyQJW_Aa_x5fgkkqsWM1odO4d6SB0QckVJURdJ0qVlAUBXvBSQcGO0IxWFSsI5-I474SIghJGT9E8pS0hhHLFhShnqF7gje98NG3zYYYmdDjU-MZ0xr5-f34l3PrdzmDTOdwMCZu-bxv7yyU8BNz7OIxxfTjk5DqMnfMOt03nTcQhA2YIMZ2jk9q0yc8P8wy93N0-Lx-K1dP943KxKizIcigcrAEsWGKkMwLWjkMFTBIL4CmTlIK3oErlHDgqqqriSnFZV0KWklNVsjN0OfX2MbyNPg16G8bY5ZeaEZkpQRlkik6UjSGl6Gvdx2Zn4rumRO-N6smozkb13qhmOQNTJmW22_j41_x_6AdhxHkh</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3066865132</pqid></control><display><type>article</type><title>A generalization of Banach’s lemma and its applications to perturbations of bounded linear operators</title><source>Springer Nature - Complete Springer Journals</source><source>Alma/SFX Local Collection</source><creator>Wang, Zi ; Ding, Jiu ; Wang, Yu-wen</creator><creatorcontrib>Wang, Zi ; Ding, Jiu ; Wang, Yu-wen</creatorcontrib><description>Let X be a Banach space and let P : X → X be a bounded linear operator. Using an algebraic inequality on the spectrum of P , we give a new sufficient condition that guarantees the existence of ( I – P ) −1 as a bounded linear operator on X , and a bound on its spectral radius is also obtained. This generalizes the classic Banach lemma. We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.</description><identifier>ISSN: 1005-1031</identifier><identifier>EISSN: 1993-0445</identifier><identifier>DOI: 10.1007/s11766-024-4872-3</identifier><language>eng</language><publisher>Singapore: Springer Nature Singapore</publisher><subject>Applications of Mathematics ; Banach spaces ; Linear operators ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Perturbation methods</subject><ispartof>Applied Mathematics-A Journal of Chinese Universities, 2024-06, Vol.39 (2), p.363-369</ispartof><rights>Editorial Committee of Applied Mathematics 2024</rights><rights>Editorial Committee of Applied Mathematics 2024.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-d2b22c2c0a6da52bd4292360c22e136112ec2787dd2d1599947746f9568641783</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11766-024-4872-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11766-024-4872-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Wang, Zi</creatorcontrib><creatorcontrib>Ding, Jiu</creatorcontrib><creatorcontrib>Wang, Yu-wen</creatorcontrib><title>A generalization of Banach’s lemma and its applications to perturbations of bounded linear operators</title><title>Applied Mathematics-A Journal of Chinese Universities</title><addtitle>Appl. Math. J. Chin. Univ</addtitle><description>Let X be a Banach space and let P : X → X be a bounded linear operator. Using an algebraic inequality on the spectrum of P , we give a new sufficient condition that guarantees the existence of ( I – P ) −1 as a bounded linear operator on X , and a bound on its spectral radius is also obtained. This generalizes the classic Banach lemma. We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.</description><subject>Applications of Mathematics</subject><subject>Banach spaces</subject><subject>Linear operators</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Perturbation methods</subject><issn>1005-1031</issn><issn>1993-0445</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1kMtOwzAQRS0EEhX0A9hZYh2wx69kWSpeUiU2sLZc2ymp0jjYyQJW_Aa_x5fgkkqsWM1odO4d6SB0QckVJURdJ0qVlAUBXvBSQcGO0IxWFSsI5-I474SIghJGT9E8pS0hhHLFhShnqF7gje98NG3zYYYmdDjU-MZ0xr5-f34l3PrdzmDTOdwMCZu-bxv7yyU8BNz7OIxxfTjk5DqMnfMOt03nTcQhA2YIMZ2jk9q0yc8P8wy93N0-Lx-K1dP943KxKizIcigcrAEsWGKkMwLWjkMFTBIL4CmTlIK3oErlHDgqqqriSnFZV0KWklNVsjN0OfX2MbyNPg16G8bY5ZeaEZkpQRlkik6UjSGl6Gvdx2Zn4rumRO-N6smozkb13qhmOQNTJmW22_j41_x_6AdhxHkh</recordid><startdate>20240601</startdate><enddate>20240601</enddate><creator>Wang, Zi</creator><creator>Ding, Jiu</creator><creator>Wang, Yu-wen</creator><general>Springer Nature Singapore</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240601</creationdate><title>A generalization of Banach’s lemma and its applications to perturbations of bounded linear operators</title><author>Wang, Zi ; Ding, Jiu ; Wang, Yu-wen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-d2b22c2c0a6da52bd4292360c22e136112ec2787dd2d1599947746f9568641783</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Applications of Mathematics</topic><topic>Banach spaces</topic><topic>Linear operators</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Perturbation methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Zi</creatorcontrib><creatorcontrib>Ding, Jiu</creatorcontrib><creatorcontrib>Wang, Yu-wen</creatorcontrib><collection>CrossRef</collection><jtitle>Applied Mathematics-A Journal of Chinese Universities</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Zi</au><au>Ding, Jiu</au><au>Wang, Yu-wen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A generalization of Banach’s lemma and its applications to perturbations of bounded linear operators</atitle><jtitle>Applied Mathematics-A Journal of Chinese Universities</jtitle><stitle>Appl. Math. J. Chin. Univ</stitle><date>2024-06-01</date><risdate>2024</risdate><volume>39</volume><issue>2</issue><spage>363</spage><epage>369</epage><pages>363-369</pages><issn>1005-1031</issn><eissn>1993-0445</eissn><abstract>Let X be a Banach space and let P : X → X be a bounded linear operator. Using an algebraic inequality on the spectrum of P , we give a new sufficient condition that guarantees the existence of ( I – P ) −1 as a bounded linear operator on X , and a bound on its spectral radius is also obtained. This generalizes the classic Banach lemma. We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.</abstract><cop>Singapore</cop><pub>Springer Nature Singapore</pub><doi>10.1007/s11766-024-4872-3</doi><tpages>7</tpages></addata></record>
fulltext	fulltext
identifier	ISSN: 1005-1031
ispartof	Applied Mathematics-A Journal of Chinese Universities, 2024-06, Vol.39 (2), p.363-369
issn	1005-1031 1993-0445
language	eng
recordid	cdi_proquest_journals_3066865132
source	Springer Nature - Complete Springer Journals; Alma/SFX Local Collection
subjects	Applications of Mathematics Banach spaces Linear operators Mathematics Mathematics and Statistics Operators (mathematics) Perturbation methods
title	A generalization of Banach’s lemma and its applications to perturbations of bounded linear operators
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-27T13%3A33%3A49IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20generalization%20of%20Banach%E2%80%99s%20lemma%20and%20its%20applications%20to%20perturbations%20of%20bounded%20linear%20operators&rft.jtitle=Applied%20Mathematics-A%20Journal%20of%20Chinese%20Universities&rft.au=Wang,%20Zi&rft.date=2024-06-01&rft.volume=39&rft.issue=2&rft.spage=363&rft.epage=369&rft.pages=363-369&rft.issn=1005-1031&rft.eissn=1993-0445&rft_id=info:doi/10.1007/s11766-024-4872-3&rft_dat=%3Cproquest_cross%3E3066865132%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3066865132&rft_id=info:pmid/&rfr_iscdi=true