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.

“The book … offers a wide range of examples and counterexamples in the theory of linear operators acting on Hilbert spaces. … The books thus covers a broad range of largely classical topics in operator theory … . The book is most likely … a reference work for its intended audience of advanced students and researchers in operator theory, as well as, no doubt, those setting exam questions on the subject.” (David Seifert, zbMATH 1512.47002, 2023)

• 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

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.

“The book … offers a wide range of examples and counterexamples in the theory of linear operators acting on Hilbert spaces. … The books thus covers a broad range of largely classical topics in operator theory … . The book is most likely … a reference work for its intended audience of advanced students and researchers in operator theory, as well as, no doubt, those setting exam questions on the subject.” (David Seifert, zbMATH 1512.47002, 2023)

• 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

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.

“The book … offers a wide range of examples and counterexamples in the theory of linear operators acting on Hilbert spaces. … The books thus covers a broad range of largely classical topics in operator theory … . The book is most likely … a reference work for its intended audience of advanced students and researchers in operator theory, as well as, no doubt, those setting exam questions on the subject.” (David Seifert, zbMATH 1512.47002, 2023)

• 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