From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."

Vectors.- Spaces
Weak Topology
Analytic Functions
Infinite Matrices
Boundedness and Invertibility
Multiplication Operators
Operator Matrices
Properties of Spectra
Examples of Spectra
Spectral Radius
Norm Topology
Operator Topologies
Strong Operator Topology
Partial Isometries
Polar Decomposition
Unilateral Shift
Cyclic Vectors
Properties of Compactness
Examples of Compactness
Subnormal Operators
Numerical Range
Unitary Dilations
Commutators
Toeplitz Operators
References
List of Symbols
Index

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