The thresholding greedy algorithm versus approximations with sizes bounded by certain functions f

Let X be a Banach space and (en)n=1∞ be a basis. For a function f in a large collection F (closed under composition), we define and characterize f-greedy and f-almost greedy bases. We study relations among these bases as f varies and show that while a basis is not almost greedy, it can be f-greedy f...

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Published in:Journal of mathematical analysis and applications 2024-11, Vol.539 (2), p.128570, Article 128570
Main Author: Chu, Hùng Việt
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Language:English
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Almost greedy
Bases
Thresholding greedy algorithm
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description Let X be a Banach space and (en)n=1∞ be a basis. For a function f in a large collection F (closed under composition), we define and characterize f-greedy and f-almost greedy bases. We study relations among these bases as f varies and show that while a basis is not almost greedy, it can be f-greedy for some f∈F. Furthermore, we prove that for all non-identity function f∈F, we have the surprising equivalencef-greedy⟺f-almost greedy. We give various examples of Banach spaces to illustrate our results.
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subjects Almost greedy
Bases
Thresholding greedy algorithm
title The thresholding greedy algorithm versus approximations with sizes bounded by certain functions f
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