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Weak weight-semi-greedy Markushevich bases

Part of: Normed linear spaces and Banach spaces; Banach lattices Approximations and expansions

Published online by Cambridge University Press:  26 June 2023

Miguel Berasategui Open the ORCID record for Miguel Berasategui [Opens in a new window]  and
Silvia Lassalle Open the ORCID record for Silvia Lassalle [Opens in a new window]
Miguel Berasategui
Affiliation:
IMAS–UBA–CONICET - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina ([email protected])
Silvia Lassalle
Affiliation:
Departamento de Matemática y Ciencias, Universidad de San Andrés, Vito Dumas 284, 1644 Victoria, Buenos Aires, Argentina IMAS–CONICET, Intendente Güiraldes S/N, 1428, Buenos Aires, Argentina ([email protected])
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Abstract

The main purpose of this paper is to study weight-semi-greedy Markushevich bases, and in particular, find conditions under which such bases are weight-almost greedy. In this context, we prove that, for a large class of weights, the two notions are equivalent. We also show that all weight semi-greedy bases are truncation quasi-greedy and weight-superdemocratic. In all of the above cases, we also bring to the context of weights the weak greedy and Chebyshev greedy algorithms—which are frequently studied in the literature on greedy approximation. In the course of our work, a new property arises naturally and its relation with squeeze symmetric and bidemocratic bases is given. In addition, we study some parameters involving the weak thresholding and Chebyshevian greedy algorithms. Finally, we give examples of conditional bases with some of the weighted greedy-type conditions we study.

Keywords

basesgreedy approximationweights

MSC classification

Primary: 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
Secondary: 46B15: Summability and bases 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 4 , August 2024 , pp. 1118 - 1179
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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