Journal of Operator Theory
Volume 88, Issue 1, Summer 2022 pp. 37-59.
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.
DOI: http://dx.doi.org/10.7900/jot.2020nov17.2322
Keywords: $M$-Basis, rank one density, $k$ point density, hereditary completeness
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