Modular Riesz bases versus Riesz bases in Hilbert C∗-modules

Abstract

In this paper we give new characterizations of modular Riesz bases in Hilbert C * -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.