Geodesic
On a Greedy Algorithm in~$L^1(0,1)$ with Regard to Subsystems of the Haar System and on $\omega$-Quasigreedy Bases
Matematičeskie zametki, Tome 88 (2010) no. 1, pp. 18-29

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All quasigreedy subsystems of the Haar system in $L^1(0,1)$ are described. The problem of renormalizing the Haar system so that it becomes a quasigreedy basis is also studied.
Keywords: greedy algorithm in $L^1(0,1)$, Haar system, $\omega$-quasigreedy basis, quasigreedy Haar subsystem, Banach space. 
@article{MZM_2010_88_1_a1,
     author = {S. L. Gogyan},
     title = {On a {Greedy} {Algorithm} in~$L^1(0,1)$ with {Regard} to {Subsystems} of the {Haar} {System} and on $\omega${-Quasigreedy} {Bases}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {18--29},
     publisher = {mathdoc},
     volume = {88},
     number = {1},
     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a1/}
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S. L. Gogyan. On a Greedy Algorithm in~$L^1(0,1)$ with Regard to Subsystems of the Haar System and on $\omega$-Quasigreedy Bases. Matematičeskie zametki, Tome 88 (2010) no. 1, pp. 18-29. http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a1/