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...
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| Published in: | Journal of approximation theory Vol. 285; p. 105831 |
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| Language: | English |
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| 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. |
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| 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 |
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| Keywords | 46B15 Partially greedy Greedy Property (A) 41A65 Almost greedy |
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| 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. |
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| SubjectTerms | Almost greedy Greedy Partially greedy Property (A) |
| Title | Variations of property (A) constants and Lebesgue-type inequalities for the weak thresholding greedy algorithms |
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