Continuous Riesz bases in Hilbert C*-modules

The paper is devoted to continuous frames and continuous Riesz basis in Hilbert C*-modules. We define a continuous Riesz basis in Hilbert C*-modules and investigate the relationship between a continuous Riesz basis and an L^۲-independent Bessel mapping. Also, we show that a continuous frame is a continuous Riesz basis if and only if it is a Riesz-type frame. Finally, we give the relation between two continuous Riesz bases in Hilbert C*-modules.

Keywords:

Hilbert C*-module , Riesz basis , continuous frame , L^۲-independent , Riesz-type frame.