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Full Description
This book focuses on spectral theory for linear operators involving bounded or unbounded demicompact linear operators acting on Banach spaces. This class played an important rule in the theory of perturbation. More precisely, it contributed in the construction of several classes of stability of essential spectra for bounded or unbounded linear operators. We should emphasize that this book is the first one dealing with the demicompactness concept and its relation with Fredholm theory for bounded and unbounded linear operators as well as block operator matrices acting on Banach spaces. Researchers, as well as graduate students in applicable analysis, will find that this book constitutes a useful survey of the fundamental principles of the subject. Nevertheless, the reader is assumed to be, at least, familiar with some related sections concerning notions like the compact, Fredholm operators, the basic tools of the weak topology, the concept of measures of weak noncompactness, etc. Otherwise, the reader is urged to consult the recommended literature in order to benefit fully from this book.
Features -
• First book dealing with demicompactness theory and its relation with Fredholm theory for bounded and unbounded linear operators as well as block operator matrices acting on Banach spaces.
• Self-contained coverage of classical and more recent classes of perturbations involving the concept of demicompactness.
• Offers a useful survey of the fundamental principles of spectral theory.
• Provides applications for problem arising in physics and which are modeled by integral or partial differential equations.
Contents
1 Basic Tools of Functional Analysis 2 Closed, Bounded, Compact and Weakly Compact Operators 3 Measures of Noncompactness MNCs 4 Fredholm and Semi-Fredholm Operators 5 Demicompact Linear Operators 6 Demicompact Nonlinear Operators 7 Demicompactness of Polynomial and Operator Matrices 8 Demicompactness and Fredholm Theory 9 Description of Essential Spectra Under Demicompactness 10 Fredholm Operator Matrices Under Demicompactness 11 Relatively Pseudo Weakly Demicompact Operators 12 Some Results on B-Fredholm and Demicompact Operators 13 Demicompactness and Restrictions 14 Generalized Weak Demicompactness and MNSS 15 Applications to Mathematical Physics Problems
