Exploring K-Riesz and K-g-Riesz bases in the context of Hilbert pro-C*-modules

Abstract

In the present research, we embark on a comprehensive inquiry into K-Riesz bases and K-g Riesz bases as they manifest within pro-C*-Hilbert modules. Adopting a unique approach, we interpret the structure of K-Riesz bases through the lens of a bounded below operator, complemented by the prototypical orthonormal basis of the Hilbert module X. In parallel, our investigation elucidates nuanced traits and pioneering perspectives of K-g-Riesz bases, steered by a bounded surjective operator and a corresponding g-orthonormal basis for X. As a culmination of our efforts, we present an enriched understanding of the dynamic interactions between K-Riesz bases and K-g-Riesz bases in this mathematical context.