Cross-Gram Matrix and Riesz Sequences in Hilbert Spaces

Abstract

This paper presents a comprehensive analysis of cross-Gram matrices in Hilbert spaces with a focus on their role in frame theory and their connection with Riesz sequences and frames. It establishes conditions for the invertibility and surjectivity of these matrices. This leads to the establishment of a reliable and useful criterion for detecting Riesz sequences in Hilbert spaces.