Characterization of 1-quasi-greedy bases
In this note we continue the study initiated in Albiac and Wojtaszczyk (2006) of greedy-like bases in the “isometric case”, i.e., in the case that the constants that arise in the context of greedy bases in their different forms are 1. Here we settle the problem to find a satisfactory characterizatio...
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| Vydané v: | Journal of approximation theory Ročník 201; s. 7 - 12 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Inc
01.01.2016
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| ISSN: | 0021-9045, 1096-0430 |
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| Abstract | In this note we continue the study initiated in Albiac and Wojtaszczyk (2006) of greedy-like bases in the “isometric case”, i.e., in the case that the constants that arise in the context of greedy bases in their different forms are 1. Here we settle the problem to find a satisfactory characterization of 1-quasi-greedy bases in Banach spaces. We show that a semi-normalized basis in a Banach space is quasi-greedy with quasi-greedy constant 1 if and only if it is unconditional with suppression-unconditional constant 1. |
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| AbstractList | In this note we continue the study initiated in Albiac and Wojtaszczyk (2006) of greedy-like bases in the “isometric case”, i.e., in the case that the constants that arise in the context of greedy bases in their different forms are 1. Here we settle the problem to find a satisfactory characterization of 1-quasi-greedy bases in Banach spaces. We show that a semi-normalized basis in a Banach space is quasi-greedy with quasi-greedy constant 1 if and only if it is unconditional with suppression-unconditional constant 1. |
| 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, Campus de Arrosadía, Pamplona, 31006, Spain – sequence: 2 givenname: J.L. surname: Ansorena fullname: Ansorena, J.L. email: joseluis.ansorena@unirioja.es organization: Department of Mathematics and Computer Sciences, Universidad de La Rioja, Edificio Luis Vives, Logroño, 26004, Spain |
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