Characterizing Riesz Bases via Biorthogonal Riesz-Fischer sequences
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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