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 ofX-Bessel systems andX-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.

On uncountable b-frames in non-separable Hilbert spaces

“…For general spaces of sequences of scalars, these matters have been treated in [21]. The case of Banach spaces of sequences of frame vectors associated with bilinear mappings has been considered in [22][23][24][25][26].…”