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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
DOI: https://doi.org/10.1090/S0002-9939-09-10169-7
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.


References [Enhancements On Off] (What's this?)

  • 1. S. J. Dilworth, N. J. Kalton, D. Kutzarova, On the existence of almost greedy bases in Banach spaces, Studia Mathematics 159(2003), N1, 67-101. MR 2030904 (2005a:46021)
  • 2. S.J. Dilworth, N.J. Kalton, D. Kutzarova, V.N. Temlyakov, The thresholding greedy algorithm, greedy bases, and duality, Constr. Approx. 19(2003), N4, 575-597. MR 1998906 (2004e:41045)
  • 3. S.J. Dilworth, D. Kutzarova, P. Wojtaszczyk, On approximate $ l_1$ systems in Banach spaces, J. Approx. Theory 114(2002), N2, 214-241. MR 1883407 (2002k:46024)
  • 4. S. Gogyan, Greedy algorithm with regard to Haar subsystems, East J. Approx. 11(2005), N2, 221-236. MR 2151616 (2006c:41041)
  • 5. G. G. Gevorkyan, A. Kamont, Two remarks on quasi-greedy bases in the space $ L_1$, J. Contemp. Math. Anal. 40(2005), N1, 2-14. MR 2265671 (2007k:46049)
  • 6. S.V. Konyagin, V.N. Temlyakov, A remark on greedy approximation in Banach spaces, East J. Approx. 5(1999), 365-379. MR 1716087 (2000j:46020)
  • 7. V. N. Temlyakov, The best $ m$-term approximation and greedy algorithms, Advances in Comp. Math. 8(1998), N3, 249-265. MR 1628182 (99f:41037)
  • 8. P. Wojtaszczyk, Greedy algorithms for general biorthogonal systems, J. Approx. Theory 107(2000), N2, 293-314. MR 1806955 (2001k:46017)

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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-09-10169-7
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.

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