Abstract:
We define various algorithms for greedy approximations by elements of an arbitrary set M in a Banach space. We study the convergence of these algorithms in a Hilbert space under various geometric conditions on M. As a consequence, we obtain sufficient conditions for the additive semigroup generated by M to be dense.
Keywords:
greedy approximation, Hilbert space, density of a semigroup.
This paper was written with the financial support of a grant of the Government of the Russian Federation (project 14.W03.31.0031). Theorem 5 was proved within the research program of RFBR (grant no. 18-01-00333a).
This publication is cited in the following 5 articles:
P. A. Borodin, “Weak Convergence of a Greedy Algorithm and the WN-Property”, Math. Notes, 113:4 (2023), 475–479
P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851
K. S. Vishnevetskiy, “Condition of coincidence between greedy approximations and m-term ones”, Moscow University Mathematics Bulletin, 77:2 (2022), 67–72
Petr A. Borodin, Eva Kopecká, “Weak Limits of Consecutive Projections and of Greedy Steps”, Proc. Steklov Inst. Math., 319 (2022), 56–63
P. A. Borodin, “Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary”, Math. Notes, 109:3 (2021), 379–385
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