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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2023 Volume 113, Issue 4, Pages 483–488 (Mi mzm13667)

Weak Convergence of a Greedy Algorithm and the WN-Property

P. A. Borodinab

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics

Abstract: 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.

UDC: 517.982.256

Received: 17.07.2022

DOI: 10.4213/mzm13667


 English version:
Mathematical Notes, 2023, 113:4, 475–479

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© Steklov Math. Inst. of RAS, 2025