On a characterization of Riesz bases via biorthogonal sequences
arXiv:1912.07774 · doi:10.1007/s00041-020-09771-5
Abstract
It is well known that a sequence in a Hilbert space is a Riesz basis if and only if it is a complete Bessel sequence with biorthogonal sequence which is also a complete Bessel sequence. Here we prove that the completeness of one (any one) of the biorthogonal sequences can be omitted in the characterization.
Some applications of the main result and related references are added