Greedy approximation for biorthogonal systems in quasi-Banach spaces

By Fernando Albiac, José L. Ansorena, Pablo M. Berná, Przemyslaw Wojtaszczyk. Dissertationes Mathematicae, 2019

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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.

Subfields: Applied Mathematics, Mathematical Physics

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