Characterization of 1-almost greedy bases
This article closes the cycle of characterizations of greedy-like bases in the “isometric” case initiated in Albiac and Wojtaszczyk (J. Approx. Theory 138(1):65–86, 2006 ) with the characterization of 1-greedy bases and continued in Albiac and Ansorena (J. Approx. Theory 201:7–12, 2016 ) with the ch...
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| Vydané v: | Revista matemática complutense Ročník 30; číslo 1; s. 13 - 24 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Milan
Springer Milan
01.01.2017
Springer Nature B.V |
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| ISSN: | 1139-1138, 1988-2807 |
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| Abstract | This article closes the cycle of characterizations of greedy-like bases in the “isometric” case initiated in Albiac and Wojtaszczyk (J. Approx. Theory 138(1):65–86,
2006
) with the characterization of 1-greedy bases and continued in Albiac and Ansorena (J. Approx. Theory 201:7–12,
2016
) with the characterization of 1-quasi-greedy bases. Here we settle the problem of providing a characterization of 1-almost greedy bases in Banach spaces. We show that a basis in a Banach space is almost greedy with almost greedy constant equal to 1 if and only if it has Property (A). This fact permits now to state that a basis is 1-greedy if and only if it is 1-almost greedy and 1-quasi-greedy. As a by-product of our work we also provide a tight estimate of the almost greedy constant of a basis in the non-isometric case. |
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| AbstractList | This article closes the cycle of characterizations of greedy-like bases in the “isometric” case initiated in Albiac and Wojtaszczyk (J. Approx. Theory 138(1):65–86,
2006
) with the characterization of 1-greedy bases and continued in Albiac and Ansorena (J. Approx. Theory 201:7–12,
2016
) with the characterization of 1-quasi-greedy bases. Here we settle the problem of providing a characterization of 1-almost greedy bases in Banach spaces. We show that a basis in a Banach space is almost greedy with almost greedy constant equal to 1 if and only if it has Property (A). This fact permits now to state that a basis is 1-greedy if and only if it is 1-almost greedy and 1-quasi-greedy. As a by-product of our work we also provide a tight estimate of the almost greedy constant of a basis in the non-isometric case. This article closes the cycle of characterizations of greedy-like bases in the “isometric” case initiated in Albiac and Wojtaszczyk (J. Approx. Theory 138(1):65–86, 2006) with the characterization of 1-greedy bases and continued in Albiac and Ansorena (J. Approx. Theory 201:7–12, 2016) with the characterization of 1-quasi-greedy bases. Here we settle the problem of providing a characterization of 1-almost greedy bases in Banach spaces. We show that a basis in a Banach space is almost greedy with almost greedy constant equal to 1 if and only if it has Property (A). This fact permits now to state that a basis is 1-greedy if and only if it is 1-almost greedy and 1-quasi-greedy. As a by-product of our work we also provide a tight estimate of the almost greedy constant of a basis in the non-isometric case. |
| Author | Ansorena, J. L. Albiac, F. |
| Author_xml | – sequence: 1 givenname: F. surname: Albiac fullname: Albiac, F. email: fernando.albiac@unavarra.es organization: Mathematics Department, Universidad Pública de Navarra – sequence: 2 givenname: J. L. surname: Ansorena fullname: Ansorena, J. L. organization: Department of Mathematics and Computer Sciences, Universidad de La Rioja |
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| Cites_doi | 10.1007/s00365-002-0525-y 10.1006/jath.2000.3512 10.1016/j.jat.2015.08.006 10.1016/j.jat.2005.09.017 10.1016/j.jat.2014.09.001 |
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| Keywords | Almost greedy basis 46B15 41A65 Quasi-greedy basis Thresholding greedy algorithm Unconditional basis Property (A) |
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| References | Albiac, Ansorena (CR2) 2016; 201 Dilworth, Kutzarova, Odell, Schlumprecht, Zsák (CR3) 2014; 188 Dilworth, Kalton, Kutzarova, Temlyakov (CR4) 2003; 19 Albiac, Wojtaszczyk (CR1) 2006; 138 Wojtaszczyk (CR6) 2000; 107 Konyagin, Temlyakov (CR5) 1999; 5 SV Konyagin (204_CR5) 1999; 5 F Albiac (204_CR2) 2016; 201 SJ Dilworth (204_CR4) 2003; 19 P Wojtaszczyk (204_CR6) 2000; 107 SJ Dilworth (204_CR3) 2014; 188 F Albiac (204_CR1) 2006; 138 |
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| Title | Characterization of 1-almost greedy bases |
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