Affiliation:
1. Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, P. R. China
Abstract
Hilbert–Schmidt frame (HS-frame) has interested some mathematicians in recent years, which is more general than g-frame. This paper addresses near Riesz and Besselian properties of HS-operator sequences. We characterize HS-frame and Riesz properties of g-operator sequences using their DSI-sequences; prove that an HS-Riesz basis is an exact HS-frame while the converse is not true, and an arbitrary HS-Riesz frame contains an HS-Riesz basis; and present the connection among near HS-Riesz property, Besselian property and the kernel space dimension of synthesis operator of an HS-operator sequence.
Funder
National Natural Science Foundation of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Information Systems,Signal Processing