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Journal of Operator Theory

Volume 88, Issue 1, Summer 2022  pp. 35-57.

Rank one density for a class of $M$-bases

Authors:  Alexey Pyshkin
Author institution: Chebyshev Laboratory, Saint Petersburg State University, 14th Line V.O. 29, Saint Petersburg, 199178, Russia and Saint Petersburg Department of RAS, Steklov Mathematical Institute, Fontanka 27, Saint Petersburg, 191023, Russia and Euler International Mathematical Institute, naber Pesochnaya 10, Saint Petersburg, 197022, Russia

Summary:  In 1990s several papers studied a strong tridiagonal $M$-basis that did not possess rank one density property. We offer a new method for the study of more generic finite-band $M$-bases, employing a graph theory framework. We determine the necessary and sufficient conditions for rank one density property in this class of $M$-bases. Also we give some sufficient conditions concerning $k$ point density property.

Keywords: $M$-Basis, rank one density, $k$ point density, hereditary completeness

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