Year: 2025
Type: article
Abstract: We consider a new version of a greedy algorithm in biorthogonal systems in separable Banach spaces. We consider approximations of an element $f$ via $m$-term greedy sum, which is constructed from the expansion by choosing the first $m$ greatest in absolute value coefficients. It is known that the greedy algorithm does not always converge to the original element. We prove a theorem showing that the new version of a greedy algorithm (called the regularized greedy algorithm) always converges to the original element in Efimov-Stechkin spaces. We also construct examples that show the significance of the conditions of the main theorem.
Source: Izvestiya Mathematics
DOI: 10.4213/im9608e
Author: Iurii Petrovich Svetlov
Institution: Lomonosov Moscow State University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G2691112575, G5476288340
OpenAlex ID: W4410373382