Aimed at a general mathematical audience, this book provides a careful exposition of recent developments in the theory of spectral decomposition. Bringing the reader from the basics up to the level of current research in the area, Lange and Wang present a readable account of the techniques used in the theory and applications of decomposable operators and related classes of operators. The book begins with a discussion of criteria for decomposable and related types of operators, and an analysis that relates and distinguishes among them. Perturbation theory of decomposable and other operators, applications to classical Hilbert space operators, quasisimilarity, and a new class of weakly decomposable operators are also discussed. The book closes with an exposition of some classical theories on invariant subspaces for subdecomposable and hyponormal operators, and a presentation of the parallel spectral theory of commuting systems.

Reviews

"The book is certainly helpful to obtain an impression of the various possible definitions of spectral decomposition properties and their innumerable interrelations."

-- Mathematical Reviews

"A well readable introduction into the subject."

-- Zentralblatt MATH

Table of Contents

• Foundations
• Perturbation theory
• Weakly decomposable operators and automatic continuity
• Invariant subspaces for subdecomposable operators
• Multivariate theory