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- W61389918 abstract "The fact that finite direct sums of two or more mutually different spaces from the family ${ell_{p} : 1le p<infty}cup c_{0}$ fail to have greedy bases is stated in [Dilworth et al., Greedy bases for Besov spaces, Constr. Approx. 34 (2011), no. 2, 281-296]. However, the concise proof that the authors give of this fundamental result in greedy approximation relies on a fallacious argument, namely the alleged uniqueness of unconditional basis up to permutation of the spaces involved. The main goal of this note is to settle the problem by providing a correct proof. For that we first show that all greedy bases in an $ell_{p}$ space have fundamental functions of the same order. As a by-product of our work we obtain that every almost greedy basis of a Banach space with unconditional basis and nontrivial type contains a greedy subbasis." @default.
- W61389918 created "2016-06-24" @default.
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- W61389918 date "2014-01-03" @default.
- W61389918 modified "2023-09-27" @default.
- W61389918 title "Non-existence of greedy bases in direct sums of mixed $ell_{p}$ spaces" @default.
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