Hilbert Space Operators: A Problem Solving Approach

This self-contained treatment of bounded linear operators on a Hilbert space provides an examination of the theory from a problem-solving viewpoint. Each chapter interweaves theoretical results with a number of problems, ranging from simple yet instructive exercises to open questions at the forefront of current research; complete solutions to all stated problems are provided.

Written in a motivating and rigorous style, the text covers much of the classical theory: it begins with the basics of invariant subspaces, linear operators, convergence, shifts, and decompositions, and then proceeds to hyponormal operators, spectral properties, and paranormal and quasireducible operators. The book concludes with a detailed presentation of the Lomonosov Theorem on nontrivial hyperinvariant subspaces for compact operators.

Some knowledge of elementary functional analysis and a familiarity with the basics of operator theory are all that is required. While this problem-solving approach to the study of Hilbert space operators is primarily aimed at graduate students, it will benefit researchers and working scientists as well, given the far-reaching applications of the subject to pure and applied mathematics, physics, engineering, economics, and statistics.