Modular Riesz bases versus Riesz bases in Hilbert $C^{\ast }$-Modules

Abstract

In this paper, we give new characterizations of modular Riesz bases in Hilbert $C^{\ast }$-modules. We prove that modular Riesz bases share many properties with Riesz bases in Hilbert spaces. Moreover we show that there are also important differences; for example, there exist exact frames that are not modular Riesz bases.

To appear in Asian-European Journal of Mathematics

References in corpus (1)

• Weak frames in Hilbert C*-modules with application in Gabor analysis