Geodesic
Weight-almost greedy bases
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 120-141.

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We introduce the notion of a weight-almost greedy basis and show that a basis for a real Banach space is $w$-almost greedy if and only if it is both quasi-greedy and $w$-democratic. We also introduce the notion of a weight-semi-greedy basis and show that a $w$-almost greedy basis is $w$-semi-greedy and that the converse holds if the Banach space has finite cotype. 
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S. J. Dilworth; D. Kutzarova; V. N. Temlyakov; B. Wallis. Weight-almost greedy bases. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 120-141. http://geodesic.mathdoc.fr/item/TM_2018_303_a9/

[1] Berná P. M., Blasco Ó., “The best $m$-term approximation with respect to polynomials with constant coefficients”, Anal. math., 43:2 (2017), 119–132 | DOI | MR | Zbl

[2] Cohen A., DeVore R. A., Hochmuth R., “Restricted nonlinear approximation”, Constr. Approx., 16:1 (2000), 85–113 | DOI | MR | Zbl

[3] Dilworth S. J., Kalton N. J., Kutzarova D., “On the existence of almost greedy bases in Banach spaces”, Stud. math., 159:1 (2003), 67–101 | DOI | MR | Zbl

[4] Dilworth S. J., Kalton N. J., Kutzarova D., Temlyakov V. N., “The thresholding greedy algorithm, greedy bases, and duality”, Constr. Approx., 19:4 (2003), 575–597 | DOI | MR | Zbl

[5] Dilworth S. J., Soto-Bajo M., Temlyakov V. N., Quasi-greedy bases and Lebesgue-type inequalities, IMI Preprint No 02, Univ. South Carol., Columbia, SC, 2012 | MR

[6] Freeman D., Odell E., Sari B., Zheng B., On spreading sequences and asymptotic structures, E-print, 2016, arXiv: 1607.03587v1 [math.FA] | MR

[7] Garrigós G., Hernándes E., Oikhberg T., “Lebesgue-type inequalities for quasi-greedy bases”, Constr. Approx., 38:3 (2013), 447–470 | DOI | MR | Zbl

[8] Kerkyacharian G., Picard D., Temlyakov V. N., “Some inequalities for the tensor product of greedy bases and weight-greedy bases”, East J. Approx., 12:1 (2006), 103–118 | MR

[9] Konyagin S. V., Temlyakov V. N., “A remark on greedy approximation in Banach spaces”, East J. Approx., 5:3 (1999), 365–379 | MR | Zbl

[10] Temlyakov V., Greedy approximation, Cambridge Univ. Press, Cambridge, 2011 | MR | Zbl

[11] Temlyakov V., Sparse approximation with bases, Adv. Courses Math. CRM Barcelona, Birkhäuser, Basel, 2015 | DOI | MR | Zbl

[12] Wojtaszczyk P., “Greedy algorithm for general biorthogonal systems”, J. Approx. Theory, 107:2 (2000), 293–314 | DOI | MR | Zbl