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arXiv · 2207.02554

On Approximation Spaces and Greedy-type Bases

Pablo M. Berná·Hung Viet Chu·Eugenio Hernández
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Abstract

The purpose of this paper is to introduce $\omega$-Chebyshev-greedy and $\omega$-partially greedy approximation classes and to study their relation with $\omega$-approximation spaces, where the latter are a generalization of the classical approximation spaces. The relation gives us sufficient conditions of when certain continuous embeddings imply different greedy-type properties. Along the way, we generalize a result by P. Wojtaszczyk as well as characterize semi-greedy Schauder bases in quasi-Banach spaces, generalizing a previous result by the first author.

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Pablo M. Berná, Hung Viet Chu, Eugenio Hernández. 2022-07-06. On Approximation Spaces and Greedy-type Bases. https://arxiv.org/abs/2207.02554

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