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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An example of an almost greedy basis in $ L^1(0,1)$


Author: Smbat Gogyan
Journal: Proc. Amer. Math. Soc. 138 (2010), 1425-1432
MSC (2000): Primary 42C30
Published electronically: November 12, 2009
MathSciNet review: 2578535
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Abstract: We give an explicit construction of an almost greedy basis of $ L^1(0,1)$, complementing the results on existence of such a basis. The basis is described in terms of the Haar basis. We construct a quasi-greedy basis in a Banach space which is isomorphic to $ L ^1(0,1)$, and then we calculate an isomorphic image of a quasi-greedy basis.


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Additional Information

Smbat Gogyan
Affiliation: Institute of Mathematics, National Academy of Sciences, 24B Marshal Baghramian Avenue, 0019 Yerevan, Armenia

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10169-7
PII: S 0002-9939(09)10169-7
Keywords: Haar system, greedy algorithm, quasi-greedy, almost greedy, $L^1(0,1)$.
Received by editor(s): April 19, 2009
Received by editor(s) in revised form: August 14, 2009
Published electronically: November 12, 2009
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.