2023/11/07 by Roumaissae Eljazzar, Eljazzar, Roumaissae, Mohamed Rossafi +1
Computer Science · Mathematics · Physics and Astronomy · #42C15 #46L05 #Advanced Algebra and Logic #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2311.04366
openalex publication_date 2023/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.