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Characterizing Riesz Bases via Biorthogonal Riesz-Fischer sequences
Published 2 Dec 2022 in math.FA | (2212.02252v1)
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'' byBessel sequences''.
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