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Biorthogonal characterization of generalized Riesz bases. (Chinese. English summary) Zbl 07821968

Summary: In this paper, we investigate the characterization of g-Riesz bases in term of g-biorthogonal sequences. We obtain that a sequence of operators is a g-Riesz basis if and only if it is a g-complete g-Bessel sequence with g-biorthogonal sequence which is also a g-complete g-Bessel sequence, and further prove that the condition for gcompleteness of one (any one) of two g-Bessel sequences can be removed from the characterization. Examples are given to illustrate the relations for g-biorthogonality, g-completeness and g-Bessel condition.

MSC:

42C15 General harmonic expansions, frames
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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