Characterization of greedy bases in Banach spaces
We shall present a new characterization of greedy bases and 1-greedy bases in terms of certain functionals defined using distances to one dimensional subspaces generated by the basis. We also introduce a new property that unifies the notions of unconditionality and democracy and allows us to recover...
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| Vydané v: | Journal of approximation theory Ročník 215; s. 28 - 39 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Inc
01.03.2017
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| ISSN: | 0021-9045, 1096-0430 |
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| Abstract | We shall present a new characterization of greedy bases and 1-greedy bases in terms of certain functionals defined using distances to one dimensional subspaces generated by the basis. We also introduce a new property that unifies the notions of unconditionality and democracy and allows us to recover a better dependence on the constants. |
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| AbstractList | We shall present a new characterization of greedy bases and 1-greedy bases in terms of certain functionals defined using distances to one dimensional subspaces generated by the basis. We also introduce a new property that unifies the notions of unconditionality and democracy and allows us to recover a better dependence on the constants. |
| Author | Blasco, Óscar Berná, Pablo M. |
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| Cites_doi | 10.1016/j.jat.2015.08.006 10.1006/jath.2000.3512 10.1016/j.jat.2005.09.017 10.1007/s13163-016-0204-3 10.1016/j.jat.2014.09.001 |
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| References | Published online 8 June 2016. F. Albiac, J.L. Ansorena, Characterization of 1-almost greedy bases, Rev. Mat. Comput. Wojtaszczyk (br000035) 2000; 107 Albiac, Wojtaszczyk (br000015) 2006; 138 Albiac, Ansorena (br000005) 2016; 201 Temlyakov (br000030) 2011; vol. 20 Konyagin, Temlyakov (br000025) 1999; 5 Dilworth, Kutzarova, Odell, Schlumprecht, Zsak (br000020) 2014; 188 Albiac (10.1016/j.jat.2016.11.008_br000005) 2016; 201 Dilworth (10.1016/j.jat.2016.11.008_br000020) 2014; 188 10.1016/j.jat.2016.11.008_br000010 Wojtaszczyk (10.1016/j.jat.2016.11.008_br000035) 2000; 107 Temlyakov (10.1016/j.jat.2016.11.008_br000030) 2011; vol. 20 Albiac (10.1016/j.jat.2016.11.008_br000015) 2006; 138 Konyagin (10.1016/j.jat.2016.11.008_br000025) 1999; 5 |
| References_xml | – volume: 201 start-page: 7 year: 2016 end-page: 12 ident: br000005 article-title: Characterization of 1-quasi greedy bases publication-title: J. Approx. Theory – reference: F. Albiac, J.L. Ansorena, Characterization of 1-almost greedy bases, Rev. Mat. Comput., – volume: 5 start-page: 365 year: 1999 end-page: 379 ident: br000025 article-title: A remark on greedy approximation in Banach spaces publication-title: East J. Approx. – volume: 107 start-page: 293 year: 2000 end-page: 314 ident: br000035 article-title: Greedy algorithm for general biorthogonal systems publication-title: J. Approx. Theory – volume: 188 start-page: 39 year: 2014 end-page: 56 ident: br000020 article-title: Renorming spaces with greedy bases publication-title: J. Approx. Theory – reference: . Published online 8 June 2016. – volume: 138 start-page: 65 year: 2006 end-page: 86 ident: br000015 article-title: Characterization of 1-greedy bases publication-title: J. Approx. Theory – volume: vol. 20 year: 2011 ident: br000030 publication-title: Greedy Approximation – volume: 201 start-page: 7 year: 2016 ident: 10.1016/j.jat.2016.11.008_br000005 article-title: Characterization of 1-quasi greedy bases publication-title: J. Approx. Theory doi: 10.1016/j.jat.2015.08.006 – volume: 107 start-page: 293 issue: 2 year: 2000 ident: 10.1016/j.jat.2016.11.008_br000035 article-title: Greedy algorithm for general biorthogonal systems publication-title: J. Approx. Theory doi: 10.1006/jath.2000.3512 – volume: 138 start-page: 65 issue: 1 year: 2006 ident: 10.1016/j.jat.2016.11.008_br000015 article-title: Characterization of 1-greedy bases publication-title: J. Approx. Theory doi: 10.1016/j.jat.2005.09.017 – ident: 10.1016/j.jat.2016.11.008_br000010 doi: 10.1007/s13163-016-0204-3 – volume: vol. 20 year: 2011 ident: 10.1016/j.jat.2016.11.008_br000030 – volume: 5 start-page: 365 year: 1999 ident: 10.1016/j.jat.2016.11.008_br000025 article-title: A remark on greedy approximation in Banach spaces publication-title: East J. Approx. – volume: 188 start-page: 39 year: 2014 ident: 10.1016/j.jat.2016.11.008_br000020 article-title: Renorming spaces with greedy bases publication-title: J. Approx. Theory doi: 10.1016/j.jat.2014.09.001 |
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| SubjectTerms | Property (A) Thresholding greedy algorithm Unconditional basis |
| Title | Characterization of greedy bases in Banach spaces |
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