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arXiv · 2212.02252

Characterizing Riesz Bases via Biorthogonal Riesz-Fischer sequences

Elias Zikkos
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Abstract

In this note we prove that if two Riesz-Fischer sequences in a separable Hilbert space $H$ are biorthogonal and one of them is complete in $H$, then both sequences are Riesz bases for $H$. This complements a recent result by D. T. Stoeva where the same conclusion holds if one replaces the phrase ``Riesz-Fischer sequences'' by ``Bessel sequences''.

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Elias Zikkos. 2022-12-02. Characterizing Riesz Bases via Biorthogonal Riesz-Fischer sequences. https://arxiv.org/abs/2212.02252

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