Spectral Theory for Linear Operators

Bilel Krichen is a Professor in the department of mathematics at the University of Sfax, Tunisia. He completed both his PhD in Mathematics in 2011 and his Habilitation in Mathematics in 2016 at the same institution. His research focuses on key areas of functional analysis, including the interplay between operator theory and fixed point theory, with applications to transport equations and other mathematical models. Prof. Dr. Krichen has been an active member of the mathematical community, notably serving as the vice president of the Tunisian Association of Applied Mathematics and Industry (ATMAI) from 2019 to 2022. His involvement with the association began in 2015, reflecting his commitment to fostering the development and application of mathematical sciences in Tunisia and beyond. A prolific scholar, Prof. Krichen has authored 88 research papers and supervised 9 graduate theses, mentoring the next generation of mathematicians. He is the author of the book Spectral Properties and Fixed Point Theory for Block Operator Matrix: Fixed Point Theory, Spectral Properties for Block Operator Matrix and Applications to Transport Equation (Scholar's Press 2014) and he is the co-author of the monograph Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications (Monographs and Research Notes in Mathematics, CRC Press Taylor and Francis, Boca Raton, 2015).

• 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

"This book could be used by a researcher in functional analysis or operator theory who wishes to familiarise themself with the theory of demicompact operators and related classes. Alternatively it could be used, together with [other resources], in a class for postgraduates with a title like “Spectral and Perturbation Theory in Banach Algebras”.-Edward L. Bach, Irish Math. Soc. Bulletin