Fernando Albiac, Jose L. Ansorena, Pablo M. Berna, Przemyslaw Wojtaszczyk
Published 2019-03-27Version 1
The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevich bases) in quasi-Banach spaces from a functional-analytic point of view. We revisit the concepts of greedy, quasi-greedy, and almost greedy bases in this comprehensive framework and provide the (nontrivial) extensions of the corresponding characterizations of those types of bases. As a by-product of our work, new properties arise, and the relations amongst them are carefully discussed.
Weaker forms of unconditionality of bases in greedy approximation
New parameters and Lebesgue-type estimates in greedy approximation
The Thresholding Greedy Algorithm versus Approximations with Sizes Bounded by Certain Functions $f$
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