Mohammed Hichem Mortad's primary research interest is operator theory. He received his Ph.D. in mathematical analysis from the University of Edinburgh in 2003.

Presents over 500 counterexamples in operator theory at varying levels of difficulty

Includes counterexamples on both bounded and unbounded linear operators, many of which are the author's original work

Divided into brief subsections, making it easy for readers to navigate the wide variety of topics included

Preface.- Part 1. Bounded Linear Operators.- Some Basic Properties.- Basic Classes of Bounded Linear Operators.- Operator Topologies.- Positive Operators.- Matrices of Bounded Operators.- (Square) Roots of Bounded Operators.- Absolute Value. Polar Decomposition.- Spectrum.- Spectral Radius. Numerical Range.- Compact Operators.- Functional Calculi.- Fuglede-Putnam Theorems and Intertwining Relations.- Operator Exponentials.- Nonnormal Operators.- Similarity and Unitary Equivalence.- The Sylvester Equation.- More Questions and Some Open Problems.- Part 2. Unbounded Linear Operators.- Basic Notions.- Closedness.- Adjoints. Symmetric Operators.- Self-adjointness.- (Arbitrary) Square Roots.- Normality.- Absolute Value. Polar Decomposition.- Unbounded Nonnormal Operators.- Commutativity.- The Fuglede-Putnam Theorems and Intertwining Relations.- Commutators.- Spectrum.- Matrices of Unbounded Operators.- Relative Boundedness.- More Questions and Some Open Problems II.- Appendix A: A Quick Review of the Fourier Transform.- Appendix B: A Word on Distributions and Sobolev Spaces.- Bibliography.- Index