g-FRAMES AND MODULAR RIESZ BASES IN HILBERT C~*-MODULES

摘要

In this paper we introduce modular Riesz basis, modular g-Riesz basis in Hilbert C~*-modules in a very natural way and we show that they share many properties with Riesz basis and g-Riesz basis in Hilbert spaces. We also found that by using the fact that every finitely or countably generated Hilbert C~*-module over a unital C~*-algebra has a standard Parseval frame, we characterize g-frames, modular Riesz bases and modular g-Riesz bases. Finally we obtain a perturbation result for modular g-Riesz bases.