Pseudo-Duals of Frames and Modular Riesz Bases in Hilbert $C^\ast$-Modules

Abstract

In the present article, duals, approximate duals and pseudo-duals (generated by bounded and not necessarily adjointable operators) of a frame in a Hilbert $C^\ast$-module are characterized and some of their properties are obtained. Especially, the ones constructed by multiplication operators are discussed and their stability under the action of morphisms is focused and some equivalent conditions for the stability are derived. Finally, we get some results on pseudo-duals of modular Riesz bases, mainly their preservation under the action of morphisms and their behavior in the presence of semi-normalized symbols are studied.

Keywords

• hilbert c*-module
• frame
• dual
• approximate dual
• pseudo-dual
• modular riesz basis