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arXiv · 1912.07774

On a characterization of Riesz bases via biorthogonal sequences

Diana T. Stoeva
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Abstract

It is well known that a sequence in a Hilbert space is a Riesz basis if and only if it is a complete Bessel sequence with biorthogonal sequence which is also a complete Bessel sequence. Here we prove that the completeness of one (any one) of the biorthogonal sequences can be omitted in the characterization.

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Diana T. Stoeva. 2020-06-15. On a characterization of Riesz bases via biorthogonal sequences. https://doi.org/10.1007/s00041-020-09771-5

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