NDLI: Weak Convergence of Greedy Algorithms in Banach Spaces

Content Provider	Semantic Scholar
Author	Dilworth, Stephen J. Kutzarova, Denka Shuman, Karen L. Temlyakov, Vladimir N. Wojtaszczyk, P.
Copyright Year	2008
Abstract	We study the convergence of certain greedy algorithms in Banach spaces. We introduce the WN property for Banach spaces and prove that the algorithms converge in the weak topology for general dictionaries in uniformly smooth Banach spaces with the WN property. We show that reflexive spaces with the uniform Opial property have the WN property. We show that our results do not extend to algorithms which employ a 'dictionary dual' greedy step.
Starting Page	609
Ending Page	628
Page Count	20
File Format	PDF HTM / HTML
DOI	10.1007/s00041-008-9034-0
Volume Number	14
Alternate Webpage(s)	http://www.mimuw.edu.pl/~wojtaszczyk/Publikacje/dkstw021907.pdf
Alternate Webpage(s)	https://faculty.math.illinois.edu/~denka/dkstw100807.pdf
Alternate Webpage(s)	http://www.math.sc.edu/~dilworth/preprints_files/dkstwjfaa08.pdf
Alternate Webpage(s)	https://www.mimuw.edu.pl/~wojtaszczyk/Publikacje/dkstw021907.pdf
Alternate Webpage(s)	http://people.math.sc.edu/dilworth/preprints_files/dkstwjfaa08.pdf
Alternate Webpage(s)	http://www.math.uiuc.edu/~denka/dkstw100807.pdf
Alternate Webpage(s)	https://doi.org/10.1007/s00041-008-9034-0
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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Weak Convergence of Greedy Algorithms in Banach Spaces