ON THE WEYL AND BROWDER THEOREMS OF BOUNDED LINEAR OPERATOR - Bouguerra, Malika; Toufik, HERAIZ: Supervisor (Mohamed Boudiaf University of M'sila, 2024)
The Weyl and Browder theorems stand as pivotal landmarks in the realm of functional analysis, offering profound insights into the spectral behavior and structural properties of bounded linear operators. Pietro Aiena's seminal contributions have significantly enriched our understanding of these theorems, unraveling their intricate connections and extending their applicability to various classes of operators. In this research endeavor, we embark on a comprehensive exploration of Aiena's work, delving deep into the nuanced implications and far-reaching consequences of the Weyl and Browder theorems. Through a meticulous examination of Aiena's results, we elucidate the underlying principles governing the spectral decomposition, essential spectra, and related spectral properties of bounded linear operators. Moreover, we investigate the interplay between these theorems and other fundamental concepts in functional analysis, such as compact operators, spectral mapping theorems, and perturbation theory. By synthesizing Aiena's insights with contemporary developments in the field, we aim to provide a unified framework for understanding the spectral theory of bounded linear operators, with implications for diverse areas including operator theory, mathematical physics, and dynamical systems. Our research not only consolidates and extends Aiena's seminal contributions but also sheds light on new avenues for theoretical exploration and practical applications in functional analysis and its myriad interdisciplinary ramifications
Keywords: The Weyl; Browder theorems; linear operator