Mathematics

Condition of coincidence between greedy approximations and $m$-term ones

K. S. Vishnevetskiy

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We give conditions on a set $M$ in a Banach space that are necessary or sufficient for the following: every element which is a sum of $n$ elements from $M$ has zero $n$-th greedy residual under greedy approximation with respect to $M$.

Key words: greedy approximations, convex sets, balanced sets, Banach space, Euclidean space.

UDC: 517.982.256

Received: 27.11.2020

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2022, 77:2, 67–72

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