Variations of property (A) constants and Lebesgue-type inequalities for the weak thresholding greedy algorithms
Albiac and Wojtaszczyk introduced property (A) to characterize 1-greedy bases. Later, Dilworth et al. generalized the concept to C-Property (A), where the case C=1 gives property (A). They (among other results) characterized greedy bases by unconditionality and C-property (A). In this paper, we exte...
Uloženo v:
| Vydáno v: | Journal of approximation theory Ročník 285; s. 105831 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Inc
01.01.2023
|
| Témata: | |
| ISSN: | 0021-9045, 1096-0430 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Albiac and Wojtaszczyk introduced property (A) to characterize 1-greedy bases. Later, Dilworth et al. generalized the concept to C-Property (A), where the case C=1 gives property (A). They (among other results) characterized greedy bases by unconditionality and C-property (A). In this paper, we extend the definition of the so-called A-property constant to (A, τ)-property constants and use the extension to obtain new estimates for various Lebesgue parameters. Furthermore, we study the relation among (A, τ)-property constants and other well-known constants when τ varies. |
|---|---|
| AbstractList | Albiac and Wojtaszczyk introduced property (A) to characterize 1-greedy bases. Later, Dilworth et al. generalized the concept to C-Property (A), where the case C=1 gives property (A). They (among other results) characterized greedy bases by unconditionality and C-property (A). In this paper, we extend the definition of the so-called A-property constant to (A, τ)-property constants and use the extension to obtain new estimates for various Lebesgue parameters. Furthermore, we study the relation among (A, τ)-property constants and other well-known constants when τ varies. |
| ArticleNumber | 105831 |
| Author | Chu, Hùng Việt |
| Author_xml | – sequence: 1 givenname: Hùng Việt orcidid: 0000-0002-9966-0038 surname: Chu fullname: Chu, Hùng Việt email: hungchu2@illinois.edu organization: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61820, USA |
| BookMark | eNp9kDtPwzAYRS0EEm3hB7B5hCHFjzzFVFW8pEoswGo59pfUIbWL7YLy70kpE0On7yGdK90zRafWWUDoipI5JTS_7eadjHNGGBvvrOT0BE0oqfKEpJycogkhjCYVSbNzNA2hI4TSLKMT5N6lNzIaZwN2Dd56twUfB3y9uMFqfEZpY8DSaryCGkK7gyQOW8DGwudO9iYaCLhxHsc14G-QH-PiIaxdr41tcesB9IBl3zpv4noTLtBZI_sAl39zht4e7l-XT8nq5fF5uVglilVFTBgAzxTjhDOdqbwExhivZZnXFa-KkuRaZ0WttVKsztOaF5KmkjUVL5pKal7yGaKHXOVdCB4asfVmI_0gKBF7Y6ITozGxNyYOxkam-McoE3_dRC9Nf5S8O5AwVvoy4EVQBqwCbTyoKLQzR-gffNqJ0A |
| CitedBy_id | crossref_primary_10_1007_s40687_024_00475_6 crossref_primary_10_1016_j_jmaa_2024_128570 |
| Cites_doi | 10.1007/s13163-016-0204-3 10.4064/sm200402-20-8 10.1007/978-3-319-31557-7 10.1007/s13163-014-0163-5 10.1007/s00365-021-09531-8 10.1016/j.jat.2005.09.017 10.1007/s00365-002-0525-y 10.4064/sm211-1-3 10.4064/sm159-1-4 10.1007/s43034-019-00023-2 10.1006/jath.2000.3512 10.1007/s13163-019-00328-9 10.1023/A:1018900431309 10.1016/j.jat.2014.09.001 10.1007/s00365-013-9209-z 10.1007/s13163-017-0221-x |
| ContentType | Journal Article |
| Copyright | 2022 Elsevier Inc. |
| Copyright_xml | – notice: 2022 Elsevier Inc. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.jat.2022.105831 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1096-0430 |
| ExternalDocumentID | 10_1016_j_jat_2022_105831 S0021904522001034 |
| GroupedDBID | --K --M --Z -~X .~1 0R~ 1B1 1RT 1~. 1~5 29J 4.4 457 4G. 5GY 5VS 6I. 6TJ 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABJNI ABMAC ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACKIV ACNCT ACRLP ADBBV ADEZE ADFGL ADMUD AEBSH AEKER AENEX AETEA AEXQZ AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CAG COF CS3 DM4 DU5 EBS EFBJH EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HVGLF HZ~ H~9 IHE IXB J1W KOM LG5 M25 M41 MHUIS MO0 N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K WH7 WUQ XOL XPP YQT ZCG ZMT ZU3 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABUFD ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN ADXHL AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c297t-2ee35c23032d5c68e2223ba86b9397806dd57bddcc2b64b37a14a2f937f9ad383 |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000878374700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0021-9045 |
| IngestDate | Sat Nov 29 07:27:54 EST 2025 Tue Nov 18 22:28:53 EST 2025 Fri Feb 23 02:38:00 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | 46B15 Partially greedy Greedy Property (A) 41A65 Almost greedy |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c297t-2ee35c23032d5c68e2223ba86b9397806dd57bddcc2b64b37a14a2f937f9ad383 |
| ORCID | 0000-0002-9966-0038 |
| ParticipantIDs | crossref_primary_10_1016_j_jat_2022_105831 crossref_citationtrail_10_1016_j_jat_2022_105831 elsevier_sciencedirect_doi_10_1016_j_jat_2022_105831 |
| PublicationCentury | 2000 |
| PublicationDate | January 2023 2023-01-00 |
| PublicationDateYYYYMMDD | 2023-01-01 |
| PublicationDate_xml | – month: 01 year: 2023 text: January 2023 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of approximation theory |
| PublicationYear | 2023 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | Berasategui, Berná, Lassalle (b4) 2021; 54 Dilworth, Kutzarova, Odell, Schlumprecht, Zsák (b11) 2014; 188 Dilworth, Kalton, Kutzarova, Temlyakov (b10) 2003; 19 Berná, Blasco, Garrigós (b6) 2017; 30 Albiac, Ansorena (b1) 2017; 30 Berná (b5) 2021; 259 Berná, Chu (b8) 2022 Dilworth, Kalton, Kutzarova (b9) 2003; 159 Khurana (b15) 2020; 11 Albiac, Kalton (b2) 2016 Albiac, Wojtaszczyk (b3) 2006; 138 Dilworth, Soto-Bajo, Temlyakov (b13) 2012; 211 Temlyakov, Yang, Ye (b18) 2011; 17 Dilworth, Kutzarova, Oikhberg (b12) 2015; 28 Garrigós, Hernández, Oikhberg (b14) 2013; 38 Konyagin, Temlyakov (b16) 2002; 28 Wojtaszczyk (b19) 2000; 107 Berná, Blasco, Garrigós, Hernández, Oikhberg (b7) 2020; 33 Temlyakov (b17) 1998; 8 Wojtaszczyk (10.1016/j.jat.2022.105831_b19) 2000; 107 Konyagin (10.1016/j.jat.2022.105831_b16) 2002; 28 Dilworth (10.1016/j.jat.2022.105831_b10) 2003; 19 Albiac (10.1016/j.jat.2022.105831_b3) 2006; 138 Dilworth (10.1016/j.jat.2022.105831_b9) 2003; 159 Albiac (10.1016/j.jat.2022.105831_b2) 2016 Albiac (10.1016/j.jat.2022.105831_b1) 2017; 30 Berná (10.1016/j.jat.2022.105831_b5) 2021; 259 Garrigós (10.1016/j.jat.2022.105831_b14) 2013; 38 Berasategui (10.1016/j.jat.2022.105831_b4) 2021; 54 Berná (10.1016/j.jat.2022.105831_b6) 2017; 30 Dilworth (10.1016/j.jat.2022.105831_b13) 2012; 211 Temlyakov (10.1016/j.jat.2022.105831_b17) 1998; 8 Khurana (10.1016/j.jat.2022.105831_b15) 2020; 11 Dilworth (10.1016/j.jat.2022.105831_b12) 2015; 28 Temlyakov (10.1016/j.jat.2022.105831_b18) 2011; 17 Dilworth (10.1016/j.jat.2022.105831_b11) 2014; 188 Berná (10.1016/j.jat.2022.105831_b7) 2020; 33 Berná (10.1016/j.jat.2022.105831_b8) 2022 |
| References_xml | – volume: 38 start-page: 447 year: 2013 end-page: 470 ident: b14 article-title: Lebesgue-type inequalities for quasi-greedy bases publication-title: Constr. Approx. – volume: 30 start-page: 13 year: 2017 end-page: 24 ident: b1 article-title: Characterization of publication-title: Rev. Mat. Complut. – volume: 54 start-page: 507 year: 2021 end-page: 528 ident: b4 article-title: Strong partially greedy bases and lebesgue-type inequalities publication-title: Constr. Approx. – volume: 28 start-page: 305 year: 2002 end-page: 328 ident: b16 article-title: Greedy approximation with regard to bases and general minimal systems publication-title: Serdica Math. J. – volume: 33 start-page: 695 year: 2020 end-page: 722 ident: b7 article-title: Lebesgue inequalities for Chebyshev thresholding greedy algorithms publication-title: Rev. Mat. Complut. – volume: 211 start-page: 41 year: 2012 end-page: 69 ident: b13 article-title: Quasi-greedy bases and Lebesgue-type inequalties publication-title: Studia Math. – volume: 28 start-page: 393 year: 2015 end-page: 409 ident: b12 article-title: Lebesgue constants for the weak greedy algorithm publication-title: Rev. Mat. Complut. – year: 2016 ident: b2 article-title: Topics in Banach Space Theory – volume: 259 start-page: 225 year: 2021 end-page: 239 ident: b5 article-title: A note on partially-greedy bases in quasi-Banach spaces publication-title: Studia Math. – year: 2022 ident: b8 article-title: On some characterizations of greedy-type bases – volume: 159 start-page: 67 year: 2003 end-page: 101 ident: b9 article-title: On the existence of almost greedy bases in Banach spaces publication-title: Studia Math. – volume: 138 start-page: 65 year: 2006 end-page: 86 ident: b3 article-title: Characterization of publication-title: J. Approx. Theory – volume: 30 start-page: 369 year: 2017 end-page: 392 ident: b6 article-title: Lebesgue inequalities for greedy algorithm in general bases publication-title: Rev. Mat. Complut. – volume: 8 start-page: 249 year: 1998 end-page: 265 ident: b17 article-title: The best publication-title: Adv. Comp. Math. – volume: 19 start-page: 575 year: 2003 end-page: 597 ident: b10 article-title: The thresholding greedy algorithm, greedy bases, and duality publication-title: Constr. Approx. – volume: 11 start-page: 101 year: 2020 end-page: 117 ident: b15 article-title: Weight-partially greedy bases and weight-property (A) publication-title: Ann. Funct. Anal. – volume: 188 start-page: 39 year: 2014 end-page: 56 ident: b11 article-title: Renorming spaces with greedy bases publication-title: J. Approx. Theory – volume: 17 start-page: 127 year: 2011 end-page: 138 ident: b18 article-title: Lebesgue-type inequalities for greedy approximation with respect to quasi-greedy bases publication-title: East J. Approx. – volume: 107 start-page: 293 year: 2000 end-page: 314 ident: b19 article-title: Greedy algorithms for general biorthogonal systems publication-title: J. Approx. Theory – volume: 30 start-page: 13 year: 2017 ident: 10.1016/j.jat.2022.105831_b1 article-title: Characterization of 1-almost greedy bases publication-title: Rev. Mat. Complut. doi: 10.1007/s13163-016-0204-3 – volume: 259 start-page: 225 year: 2021 ident: 10.1016/j.jat.2022.105831_b5 article-title: A note on partially-greedy bases in quasi-Banach spaces publication-title: Studia Math. doi: 10.4064/sm200402-20-8 – year: 2016 ident: 10.1016/j.jat.2022.105831_b2 doi: 10.1007/978-3-319-31557-7 – volume: 28 start-page: 393 year: 2015 ident: 10.1016/j.jat.2022.105831_b12 article-title: Lebesgue constants for the weak greedy algorithm publication-title: Rev. Mat. Complut. doi: 10.1007/s13163-014-0163-5 – volume: 54 start-page: 507 year: 2021 ident: 10.1016/j.jat.2022.105831_b4 article-title: Strong partially greedy bases and lebesgue-type inequalities publication-title: Constr. Approx. doi: 10.1007/s00365-021-09531-8 – volume: 138 start-page: 65 year: 2006 ident: 10.1016/j.jat.2022.105831_b3 article-title: Characterization of 1-greedy bases publication-title: J. Approx. Theory doi: 10.1016/j.jat.2005.09.017 – year: 2022 ident: 10.1016/j.jat.2022.105831_b8 – volume: 19 start-page: 575 year: 2003 ident: 10.1016/j.jat.2022.105831_b10 article-title: The thresholding greedy algorithm, greedy bases, and duality publication-title: Constr. Approx. doi: 10.1007/s00365-002-0525-y – volume: 211 start-page: 41 year: 2012 ident: 10.1016/j.jat.2022.105831_b13 article-title: Quasi-greedy bases and Lebesgue-type inequalties publication-title: Studia Math. doi: 10.4064/sm211-1-3 – volume: 159 start-page: 67 year: 2003 ident: 10.1016/j.jat.2022.105831_b9 article-title: On the existence of almost greedy bases in Banach spaces publication-title: Studia Math. doi: 10.4064/sm159-1-4 – volume: 11 start-page: 101 year: 2020 ident: 10.1016/j.jat.2022.105831_b15 article-title: Weight-partially greedy bases and weight-property (A) publication-title: Ann. Funct. Anal. doi: 10.1007/s43034-019-00023-2 – volume: 107 start-page: 293 year: 2000 ident: 10.1016/j.jat.2022.105831_b19 article-title: Greedy algorithms for general biorthogonal systems publication-title: J. Approx. Theory doi: 10.1006/jath.2000.3512 – volume: 33 start-page: 695 year: 2020 ident: 10.1016/j.jat.2022.105831_b7 article-title: Lebesgue inequalities for Chebyshev thresholding greedy algorithms publication-title: Rev. Mat. Complut. doi: 10.1007/s13163-019-00328-9 – volume: 8 start-page: 249 year: 1998 ident: 10.1016/j.jat.2022.105831_b17 article-title: The best m-term approximation and greedy algorithms publication-title: Adv. Comp. Math. doi: 10.1023/A:1018900431309 – volume: 17 start-page: 127 year: 2011 ident: 10.1016/j.jat.2022.105831_b18 article-title: Lebesgue-type inequalities for greedy approximation with respect to quasi-greedy bases publication-title: East J. Approx. – volume: 188 start-page: 39 year: 2014 ident: 10.1016/j.jat.2022.105831_b11 article-title: Renorming spaces with greedy bases publication-title: J. Approx. Theory doi: 10.1016/j.jat.2014.09.001 – volume: 38 start-page: 447 year: 2013 ident: 10.1016/j.jat.2022.105831_b14 article-title: Lebesgue-type inequalities for quasi-greedy bases publication-title: Constr. Approx. doi: 10.1007/s00365-013-9209-z – volume: 30 start-page: 369 year: 2017 ident: 10.1016/j.jat.2022.105831_b6 article-title: Lebesgue inequalities for greedy algorithm in general bases publication-title: Rev. Mat. Complut. doi: 10.1007/s13163-017-0221-x – volume: 28 start-page: 305 year: 2002 ident: 10.1016/j.jat.2022.105831_b16 article-title: Greedy approximation with regard to bases and general minimal systems publication-title: Serdica Math. J. |
| SSID | ssj0011551 |
| Score | 2.334477 |
| Snippet | Albiac and Wojtaszczyk introduced property (A) to characterize 1-greedy bases. Later, Dilworth et al. generalized the concept to C-Property (A), where the case... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 105831 |
| SubjectTerms | Almost greedy Greedy Partially greedy Property (A) |
| Title | Variations of property (A) constants and Lebesgue-type inequalities for the weak thresholding greedy algorithms |
| URI | https://dx.doi.org/10.1016/j.jat.2022.105831 |
| Volume | 285 |
| WOSCitedRecordID | wos000878374700001&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: ScienceDirect Freedom Collection - Elsevier customDbUrl: eissn: 1096-0430 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011551 issn: 0021-9045 databaseCode: AIEXJ dateStart: 20211212 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1JT9tAFB6loYf2gIC2KmXRHIrUFhmRGS8zRxOBoGoRB4pyc2czJI2cKHFofn7feLyxVeXQi2VZ9os178v4m7d8g9BHqaUwqTr0uAmM5wsiPZYK4xEN32sRWn0YWWw2EZ2fs8GAX3Q6P6temNtxlGVsueTT_-pquAbOtq2zz3B3bRQuwDk4HY7gdjj-k-OvYPXb1LdNbbB9lhc5_diGAJQjhLnTZv4Gozu_XhivCMUC43RNlrB8rusPfxvxy27nY-ZlpmoflugwN--L8fVkNsxvSr3zhwy30CtfDl1zpGuZrAP4_ZtF8dWzifojDkavhkXOPt7r9_dimrejEYS2ohFVd4At-XASkdUMS1jQmiOB0TE38z-Yvl0kYXQwErbMlZCD5t67Utn3PmF1YWFVszZKwERiTSTOxAu0QqKAsy5aic-OB1_rTJOljK4MyL13lfkuagDvvcfj3KXFRy7X0Go5zDh2AFhHHZNtoNffaxXe-Rs0aaCAJymuoIA_xZ9xDQMMMMB3YIDbMMAAAww2sYUBbsMAOxjgBgZv0Y-T48v-qVdusOEpwqPcI8bQQMEilBIdqJAZSxalYKHk1CpThVoHkdRaKSJDX9JI9ODfnAKjTbnQlNF3qJtNMvMe4R73BZWKS2HlkiJYdvg927TMtLGVkHoTHVZDl6hSfd5ugjJOnnTZJvpSPzJ10it_u9mv_JGU3NFxwgSw9fRjH57zG1voVQP5bdTNZwuzg16q23w4n-2WwPoDinaPOQ |
| 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=Variations+of+property+%28A%29+constants+and+Lebesgue-type+inequalities+for+the+weak+thresholding+greedy+algorithms&rft.jtitle=Journal+of+approximation+theory&rft.au=Chu%2C+H%C3%B9ng+Vi%C3%AA%CC%A3t&rft.date=2023-01-01&rft.issn=0021-9045&rft.volume=285&rft.spage=105831&rft_id=info:doi/10.1016%2Fj.jat.2022.105831&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_jat_2022_105831 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0021-9045&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0021-9045&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0021-9045&client=summon |