Spectral inclusion properties of the numerical range in a space with an indefinite metric

In this paper the numerical range of operators (possibly unbounded) in an indefinite inner product space is studied. In particular, we show that the spectrums of bounded positive operators (or the spectrum of unbounded uniformly I -positive operators) are contained in the closure of the I -numerical...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Linear algebra and its applications Jg. 435; H. 5; S. 1131 - 1136
Hauptverfasser:	Wu, Deyu, Chen, Alatancang
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Amsterdam Elsevier Inc 01.09.2011 Elsevier
Schlagworte:	Algebra Exact sciences and technology Linear and multilinear algebra, matrix theory Mathematical analysis Mathematics Operator theory Sciences and techniques of general use The [formula omitted]-numerical range The indefinite inner product space The numerical range The uniformly [formula omitted]-positive operator 47A12 The indefinite inner product space The uniformly I -positive operator 47B50 The numerical range The I -numerical range Closure Spectral properties Bounded operator Indefinite inner product Spectrum Prehilbertian space Numerical range Indefinite metric Eigenvalue problem The G-numerical range Hausdorff space The uniformly ?-positive operator Positive operator
ISSN:	0024-3795
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Abstract	In this paper the numerical range of operators (possibly unbounded) in an indefinite inner product space is studied. In particular, we show that the spectrums of bounded positive operators (or the spectrum of unbounded uniformly I -positive operators) are contained in the closure of the I -numerical range.
AbstractList	In this paper the numerical range of operators (possibly unbounded) in an indefinite inner product space is studied. In particular, we show that the spectrums of bounded positive operators (or the spectrum of unbounded uniformly I -positive operators) are contained in the closure of the I -numerical range.
Author	Wu, Deyu Chen, Alatancang
Author_xml	– sequence: 1 givenname: Deyu surname: Wu fullname: Wu, Deyu email: wudeyu2585@163.com – sequence: 2 givenname: Alatancang surname: Chen fullname: Chen, Alatancang
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24299033$$DView record in Pascal Francis
BookMark	eNp9kLtOAzEQRV0EiQT4ADo3lFnG9r4sKhTxkiJRAAWV5XjHxNHGu7IdEH-Po0BDkWqk0T2juWdGJn7wSMglg4IBq683Ra91wYGxAngBlZiQKQAv56KR1SmZxbgBgLIBPiXvLyOaFHRPnTf9LrrB0zEMI4bkMNLB0rRG6ndbDM7kVND-A3OWahpHbZB-ubSm2udVh9Z5l5BuMeXwOTmxuo948TvPyNv93evicb58fnha3C7nRvAmzVGCaRm2nZbWriroaom1kFh2XbVqNANTo9WNAEAmKq2btjQMJecZtFVbizNydbg76pg_tPlD46Iag9vq8K14yaUEIXKuOeRMGGIMaJVxSadcONd3vWKg9vbURmV7am9PAVfZXibZP_Lv-DHm5sBgrv7pMKhoHHqDnQtZuOoGd4T-AT3VjKs
CODEN	LAAPAW
CitedBy_id	crossref_primary_10_1007_s10114_018_7294_4 crossref_primary_10_1007_s10255_012_0195_x crossref_primary_10_1016_j_laa_2012_10_048 crossref_primary_10_1007_s10255_018_0736_z crossref_primary_10_12677_AAM_2019_84095 crossref_primary_10_12677_AAM_2014_32012 crossref_primary_10_1088_1674_1056_24_8_084601 crossref_primary_10_1007_s43034_024_00367_4
Cites_doi	10.13001/1081-3810.1000 10.11650/twjm/1500574945 10.1080/0308108031000134981 10.1016/0024-3795(81)90169-5 10.13001/1081-3810.1013 10.1016/j.laa.2004.04.021
ContentType	Journal Article
Copyright	2011 Elsevier Inc. 2015 INIST-CNRS
Copyright_xml	– notice: 2011 Elsevier Inc. – notice: 2015 INIST-CNRS
DBID	6I. AAFTH AAYXX CITATION IQODW
DOI	10.1016/j.laa.2011.02.053
DatabaseName	ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef Pascal-Francis
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Mathematics
EndPage	1136
ExternalDocumentID	24299033 10_1016_j_laa_2011_02_053 S0024379511001881
GrantInformation_xml	– fundername: SPH-IMU grantid: Z20090103 – fundername: NNSF of China grantid: 10962004 – fundername: NSF of Inner Mongolia grantid: 2010MS0108
GroupedDBID	--K --M --Z -~X .~1 0R~ 0SF 1B1 1RT 1~. 1~5 29L 4.4 457 4G. 5GY 5VS 6I. 6TJ 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAFTH AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AASFE AAXKI AAXUO ABAOU ABDPE ABEFU ABFNM ABJNI ABMAC ABVKL ABXDB ACDAQ ACGFS ACRLP ADBBV ADEZE ADIYS ADMUD ADVLN AEBSH AEKER AENEX AEXQZ AFFNX AFJKZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJOXV AKRWK ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 DU5 EBS EFJIC EJD EO8 EO9 EP2 EP3 F5P FA8 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HVGLF HZ~ IHE IXB J1W KOM M26 M41 MCRUF MHUIS MO0 MVM N9A NCXOZ O-L O9- OAUVE OHT OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SES SEW SPC SPCBC SSW SSZ T5K T9H TN5 TWZ WH7 WUQ XPP YQT ZMT ~G- 9DU AATTM AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AETEA AEUPX AFPUW AGQPQ AIGII AIIUN AKBMS AKYEP ANKPU APXCP CITATION EFKBS EFLBG ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH
ID	FETCH-LOGICAL-c327t-e90c81e8da9ffb50d69e639e4dd5b7a10c6efa7300e135aa784c1e922e90f5863
ISICitedReferencesCount	12
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000292438800017&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0024-3795
IngestDate	Mon Jul 21 09:13:46 EDT 2025 Tue Nov 18 21:08:35 EST 2025 Sat Nov 29 05:08:56 EST 2025 Tue Dec 03 03:44:25 EST 2024
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	5
Keywords	47A12 The indefinite inner product space The uniformly I -positive operator 47B50 The numerical range The I -numerical range Closure Spectral properties Bounded operator Indefinite inner product Spectrum Prehilbertian space Numerical range Indefinite metric Eigenvalue problem The G-numerical range Hausdorff space The uniformly ?-positive operator Positive operator
Language	English
License	http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 CC BY 4.0
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c327t-e90c81e8da9ffb50d69e639e4dd5b7a10c6efa7300e135aa784c1e922e90f5863
OpenAccessLink	https://dx.doi.org/10.1016/j.laa.2011.02.053
PageCount	6
ParticipantIDs	pascalfrancis_primary_24299033 crossref_citationtrail_10_1016_j_laa_2011_02_053 crossref_primary_10_1016_j_laa_2011_02_053 elsevier_sciencedirect_doi_10_1016_j_laa_2011_02_053
PublicationCentury	2000
PublicationDate	2011-09-01
PublicationDateYYYYMMDD	2011-09-01
PublicationDate_xml	– month: 09 year: 2011 text: 2011-09-01 day: 01
PublicationDecade	2010
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	Linear algebra and its applications
PublicationYear	2011
Publisher	Elsevier Inc Elsevier
Publisher_xml	– name: Elsevier Inc – name: Elsevier
References	Azizov, Iokhvidov (b0050) 1989 Bayasgalan (b0045) 1991; 57 Bebiano, Lemos, da Providência, Soares (b0025) 2005; 399 Bebiano, Lemos, da Providência, Soares (b0030) 2004; 52 Bognar (b0015) 1974 Li, Rodman (b0005) 1998; 3 Li, Tsing, Uhlig (b0010) 1996; 1 Bebiano (10.1016/j.laa.2011.02.053_b0030) 2004; 52 Tam (10.1016/j.laa.2011.02.053_b0035) 2001; 72 Bayasgalan (10.1016/j.laa.2011.02.053_b0045) 1991; 57 Li (10.1016/j.laa.2011.02.053_b0010) 1996; 1 Bognar (10.1016/j.laa.2011.02.053_b0015) 1974 Fiedler (10.1016/j.laa.2011.02.053_fs010) 1981; 37 Azizov (10.1016/j.laa.2011.02.053_b0050) 1989 Tam (10.1016/j.laa.2011.02.053_b0040) 2001; 5 Bebiano (10.1016/j.laa.2011.02.053_b0025) 2005; 399 Li (10.1016/j.laa.2011.02.053_b0005) 1998; 3
References_xml	– year: 1989 ident: b0050 article-title: Linear Operators in Spaces with an Indefinite Metric – volume: 57 start-page: 7 year: 1991 end-page: 9 ident: b0045 article-title: The numerical range of linear operators in spaces with an indefinite metric publication-title: Acta Math. Hungar. – volume: 399 start-page: 17 year: 2005 end-page: 34 ident: b0025 article-title: On the geometry of numerical ranges in spaces with an indefinite inner product publication-title: Linear Algebra Appl. – volume: 3 start-page: 31 year: 1998 end-page: 47 ident: b0005 article-title: Shapes and computer generation of numerical ranges of Krein space operators publication-title: Electron. J. Linear Algebra – volume: 52 start-page: 203 year: 2004 end-page: 233 ident: b0030 article-title: On generalized numerical ranges of operators on an indefinite inner product space publication-title: Linear and Multilinear Algebra – volume: 1 start-page: 1 year: 1996 end-page: 17 ident: b0010 article-title: Numerical ranges of an operator in an indefinite inner product space publication-title: Electron. J. Linear Algebra – year: 1974 ident: b0015 article-title: Indefinite Inner Product Spaces – volume: 1 start-page: 1 year: 1996 ident: 10.1016/j.laa.2011.02.053_b0010 article-title: Numerical ranges of an operator in an indefinite inner product space publication-title: Electron. J. Linear Algebra doi: 10.13001/1081-3810.1000 – year: 1974 ident: 10.1016/j.laa.2011.02.053_b0015 – volume: 57 start-page: 7 year: 1991 ident: 10.1016/j.laa.2011.02.053_b0045 article-title: The numerical range of linear operators in spaces with an indefinite metric publication-title: Acta Math. Hungar. – year: 1989 ident: 10.1016/j.laa.2011.02.053_b0050 – volume: 5 start-page: 497 year: 2001 ident: 10.1016/j.laa.2011.02.053_b0040 article-title: On the shape of numerical range associated with Lie groups publication-title: Taiwanese J. Math doi: 10.11650/twjm/1500574945 – volume: 52 start-page: 203 year: 2004 ident: 10.1016/j.laa.2011.02.053_b0030 article-title: On generalized numerical ranges of operators on an indefinite inner product space publication-title: Linear and Multilinear Algebra doi: 10.1080/0308108031000134981 – volume: 37 start-page: 81 year: 1981 ident: 10.1016/j.laa.2011.02.053_fs010 article-title: Geometry of the numerical range of matrices publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(81)90169-5 – volume: 72 start-page: 1 year: 2001 ident: 10.1016/j.laa.2011.02.053_b0035 article-title: Convexity of generalized numerical range associated with a compact Lie group publication-title: J. Austral. Math. Soc. – volume: 3 start-page: 31 year: 1998 ident: 10.1016/j.laa.2011.02.053_b0005 article-title: Shapes and computer generation of numerical ranges of Krein space operators publication-title: Electron. J. Linear Algebra doi: 10.13001/1081-3810.1013 – volume: 399 start-page: 17 year: 2005 ident: 10.1016/j.laa.2011.02.053_b0025 article-title: On the geometry of numerical ranges in spaces with an indefinite inner product publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2004.04.021
SSID	ssj0004702
Score	2.0185747
Snippet	In this paper the numerical range of operators (possibly unbounded) in an indefinite inner product space is studied. In particular, we show that the spectrums...
SourceID	pascalfrancis crossref elsevier
SourceType	Index Database Enrichment Source Publisher
StartPage	1131
SubjectTerms	Algebra Exact sciences and technology Linear and multilinear algebra, matrix theory Mathematical analysis Mathematics Operator theory Sciences and techniques of general use The [formula omitted]-numerical range The indefinite inner product space The numerical range The uniformly [formula omitted]-positive operator
Title	Spectral inclusion properties of the numerical range in a space with an indefinite metric
URI	https://dx.doi.org/10.1016/j.laa.2011.02.053
Volume	435
WOSCitedRecordID	wos000292438800017&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 issn: 0024-3795 databaseCode: AIEXJ dateStart: 19950101 customDbUrl: isFulltext: true dateEnd: 20180131 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0004702 providerName: Elsevier
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Nb9MwFLeg4wBCiK-J8TH5wIkqk-M4sX2cUNFAMHFYoTtFrmNLnaKsalO0P5_n2HGyCQYcuERtZDeV3y_Pz-_j9xB6y6kijBMD4GU6YZrRRFbCJEYvdWErS3XXkuXbZ356KhYL-TWkjW27dgK8acTVlVz_V1HDPRC2K539B3HHH4Ub8BmEDlcQO1z_SvCuo3zruTR0vXPOMJeEtXb5055g1pmazc5HaurpxlUXOK-HmoJygbc8VLtNHY-iXTmT1LWZ3qz02I6FI6xjAHJNQuC4HSMQ43B4NJFn5_Pp93kMdpzMfGZBrVrnTwk7ZzV4UuXY8dBXxIy1K2Ugc980s9euzLORBBjlI12ZpkH_m_5r8Uud7t0LF0e1UoFylR4RzzB8nT_7xr4Wsw1pt-dm2V20R3kuxQTtHX-cLT4N9bOcBFZ5___76HeXB3jjsb-zXx6u1RakZn07lJGNcvYYPQqHC3zsQfEE3THNU_TgS2Tm3T5D5z08cIQHHuCBLy2GwTjCA3fwgLFY4Q4e2MEDqwYP8MAeHs_R_MPs7P1JEtprJDqjvE2MJFqkRlRKWrvMSVVIA_aqYVWVL7lKiS6MVa6fgUmzXCkumE6NpBQm2lwU2T6aNJeNeYFwnio4iesqc9MFrWTGLNewfywp0TQtDhDpF63UgXvetUCpyz7J8KKEdS7dOpeElrDOB-hdnLL2xCu3DWa9JMpgOXqLsAQQ3Tbt8JrU4oN6xLz804BX6P7warxGk3azM2_QPf2jXW03hwFnPwGtXJfr
linkProvider	Elsevier
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Spectral+inclusion+properties+of+the+numerical+range+in+a+space+with+an+indefinite+metric&rft.jtitle=Linear+algebra+and+its+applications&rft.au=DEYU+WU&rft.au=CHEN%2C+Alatancang&rft.date=2011-09-01&rft.pub=Elsevier&rft.issn=0024-3795&rft.volume=435&rft.issue=5&rft.spage=1131&rft.epage=1136&rft_id=info:doi/10.1016%2Fj.laa.2011.02.053&rft.externalDBID=n%2Fa&rft.externalDocID=24299033
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0024-3795&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0024-3795&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0024-3795&client=summon