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arXiv · 1901.02422

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

Alexey Pyshkin
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Abstract

In the early 1990s the works of Larson, Wogen and Argyros, Lambrou, Longstaff disclosed an example of a strong $M$-basis that did not admit a linear summation method. We study a class of $M$-bases $\mathfrak{F}=\{f_n\}_{n=1}^\infty$ in the Hilbert space that generalizes the Larson--Wogen system. We determine the conditions under which $\mathfrak{F}$ admits a linear summation method. In order to do that we employ some of the graph theory techniques.

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Alexey Pyshkin. 2019-01-08. Rank one density property for a class of $M$-bases. https://arxiv.org/abs/1901.02422

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