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Renorming spaces with greedy bases. (English) Zbl 1305.41033

Greedy methods are one of the central approaches in approximation theory and applications. For this, greedy bases are required to generate the appropriate approximation sub-spaces of Banach spaces. Greedy or democracy constants are associated with these bases, where for instance the greedy constant is the factor by which the error of the greedy approximation and the smallest possible error differ, and improvements are derived in this article for the constants of such bases.

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A44 Best constants in approximation theory
41A50 Best approximation, Chebyshev systems
46B03 Isomorphic theory (including renorming) of Banach spaces
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References:

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