Characterizing Riesz bases via biorthogonal Bessel sequences

E. Zikkos

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Recently D.T. Stoeva proved that if two Bessel 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 improves a well known result where completeness is assumed on both sequences. In this note we present an alternative proof of Stoeva’s result which is quite short and elementary, based on the notion of Riesz-Fischer sequences.

Original languageBritish English
Pages (from-to)377-380
Number of pages4
JournalCarpathian Mathematical Publications
Volume15
Issue number2
DOIs
StatePublished - 30 Dec 2023

Keywords

  • Bessel sequence
  • biorthogonal sequence
  • completeness
  • Riesz basis
  • Riesz sequence
  • Riesz-Fischer sequence

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