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Other titles in the Grundlehren Der Mathematischen Wissenschaften series:
Hilbert Space Problem Bookby Paul R. Halmos
Synopses & Reviews
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."
Written for the active reader with some background in the topic, this book presents problems in Hilbert space theory, with definitions, corollaries and historical remarks, hints, proofs, answers and constructions.
Bibliography: p. 347-354.
Table of Contents
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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