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1998•arXiv (Cornell University)Open access

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

Roman Vershynin

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Abstract

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

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

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

Key concepts: Basis (linear algebra), Banach space, Mathematics, Class (philosophy), Pure mathematics, Space (punctuation), Discrete mathematics, Computer science

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