On constructions of strong and uniformly minimal M-bases in Banach spaces

DOI10.1007/PL00000409zbMATH Open0981.46010arXivmath/9804066OpenAlexW2133790380MaRDI QIDQ1973462

Roman Vershynin

Publication date: 1 March 2002

Published in: Archiv der Mathematik (Search for Journal in Brave)

Abstract: We find a natural class of transformations ("flattened perturbations") of a norming M-basis in a Banach space X, which give a strong norming M-basis in X. This simplifies and generalizes the positive answer to the "strong M-basis problem" solved by P. Terenzi. We also show that in general one cannot achieve uniformly minimality applying standard transformations to a given norming M-basis, despite of the existence in X a uniformly minimal strong M-bases.

Full work available at URL: https://arxiv.org/abs/math/9804066

zbMATH Keywords

biorthogonal system\(M\)-basisbounded block perturbationflattened perturbations

Mathematics Subject Classification ID

Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items (3)

Some counterexamples concerning strong \(M\)-bases of Banach spaces ⋮ On the relations between Auerbach or almost Auerbach Markushevich systems and Schauder bases ⋮ SKIPPED BLOCKING AND OTHER DECOMPOSITIONS IN BANACH SPACES

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