ON THE WEYL AND BROWDER THEOREMS OF BOUNDED LINEAR OPERATOR
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Date
2024-06-10
Journal Title
Journal ISSN
Volume Title
Publisher
Mohamed Boudiaf University of M'sila
Abstract
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
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Keywords
The Weyl, Browder theorems, linear operator