Exploring K-Riesz and K-g-Riesz bases in the context of Hilbert pro-C*-modules
Functional Analysis
2023-11-09 v1
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.
Keywords
Cite
@article{arxiv.2311.04366,
title = {Exploring K-Riesz and K-g-Riesz bases in the context of Hilbert pro-C*-modules},
author = {Roumaissae Eljazzar and Mohamed Rossafi},
journal= {arXiv preprint arXiv:2311.04366},
year = {2023}
}