Geodesic
Weak Convergence of a Greedy Algorithm and the WN-Property
Matematičeskie zametki, Tome 113 (2023) no. 4, pp. 483-488

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We study the weak convergence of a greedy algorithm of approximation by a given set in a Banach space. It is proved that the greedy algorithm of approximation by a strongly norm-reducing set in a uniformly smooth Banach space with the WN-property weakly converges. In an arbitrary separable Banach space without the WN-property, we construct an example of a strongly norm-reducing set such that the greedy algorithm of approximation by this set does not weakly converge for some initial element. Bibliography: 6 titles.
Keywords: greedy approximations, Banach space, weak convergence, WN-property. 
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     author = {P. A. Borodin},
     title = {Weak {Convergence} of a {Greedy} {Algorithm} and the {WN-Property}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_4_a0/}
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P. A. Borodin. Weak Convergence of a Greedy Algorithm and the WN-Property. Matematičeskie zametki, Tome 113 (2023) no. 4, pp. 483-488. http://geodesic.mathdoc.fr/item/MZM_2023_113_4_a0/