An Operator Theory Problem Book

This book is for third and fourth year university mathematics students (and Master students) as well as lecturers and tutors in mathematics and anyone who needs the basic facts on Operator Theory (e.g. Quantum Mechanists). The main setting for bounded linear operators here is a Hilbert space. There is, however, a generous part on General Functional Analysis (not too advanced though). There is also a chapter on Unbounded Closed Operators.

The book is divided into two parts. The first part contains essential background on all of the covered topics with the sections: True or False Questions, Exercises, Tests and More Exercises. In the second part, readers may find answers and detailed solutions to the True or False Questions, Exercises and Tests.

Another virtue of the book is the variety of the topics and the exercises and the way they are tackled. In many cases, the approaches are different from what is known in the literature. Also, some very recent results from research papers are included.

Contents:

• Normed Vector Spaces: Banach Spaces
• Bounded Linear Operators on Banach Spaces
• Hilbert Spaces
• Classes of Linear Operators on Hilbert Spaces
• Positive Operators: Square Root
• Absolute Value: Polar Decomposition of an Operator
• Spectrum of an Operator
• Spectral Radius and Numerical Range
• Compact Operators
• Closed Operators
• Functional Calculi
• Hyponormal Operators
• Similarities of Operators

Readership: Undergraduate students, lecturers and tutors in operator theory and functional analysis.
Key Features:

• For example, the treatment of the chapters on square roots and absolute values of operators is unique. So is the chapter on hyponormal operators
• Many exercises with solutions that are very detailed, and so many topics are presented in a simple way to students
• Results are up to date