On Bessel and Riesz-Fisher systems with respect to Banach space of vector-valued sequences

Abstract

The paper deals with Bessel systems and Riesz-Fisher systems in Banach spaces with respect to some Banach space of vector-valued sequences. The notions of ˜ X -Bessel systems and ˜ X -Riesz-Fisher systems were introduced and the characterization of such systems were established. ˜ X -frames and ˜ X -Riesz g -bases are also studied in this paper. The relations between them are obtained.