Abstract
We prove that if [Formula Presented] is a complete Riesz-Fischer sequence in a separable Hilbert space H, then [Formula Presented] is closed in H if and only if [Formula Presented] has a biorthogonal Riesz sequence. If the latter is also complete in H, then [Formula Presented] is a Riesz basis for H.
| Original language | British English |
|---|---|
| Pages (from-to) | 124-131 |
| Number of pages | 8 |
| Journal | Problemy Analiza |
| Volume | 13(31) |
| Issue number | 1 |
| DOIs | |
| State | Published - 2024 |
Keywords
- Bessel sequences
- biorthogonal sequences
- Riesz bases
- Riesz sequences
- Riesz-Fischer sequences
- сompleteness
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