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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Vydáno v:	Journal of mathematical analysis and applications Ročník 539; číslo 2; s. 128570
Hlavní autor:	Chu, Hùng Việt
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 15.11.2024
Témata:	Almost greedy Bases Thresholding greedy algorithm Bases Thresholding greedy algorithm Almost greedy
ISSN:	0022-247X, 1096-0813
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2024.128570