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In the present research, we embark on a comprehensive inquiry into K-Rieszbases 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 throughthe lens of a bounded below operator, complemented by the prototypicalorthonormal basis of the Hilbert module X. In parallel, our investigationelucidates nuanced traits and pioneering perspectives of K-g-Riesz bases,steered by a bounded surjective operator and a corresponding g-orthonormalbasis for X. As a culmination of our efforts, we present an enrichedunderstanding of the dynamic interactions between K-Riesz bases and K-g-Rieszbases in this mathematical context.

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