Introduction to Hilbert Space and the Theory of Spectral Multiplicity: Second Edition (Dover Books on Mathematics) 2nd Edition by Paul R. Halmos (PDF)

Description

This concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. Author Paul R. Halmos notes in the Preface that his motivation in writing this text was to make available to a wider audience the results of the third chapter, the so-called multiplicity theory. The theory as he presents it deals with arbitrary spectral measures, including the multiplicity theory of normal operators on a not necessarily separable Hilbert space. His explication covers, as another useful special case, the multiplicity theory of unitary representations of locally compact abelian groups.Suitable for advanced undergraduates and graduate students in mathematics, this volume’s sole prerequisite is a background in measure theory. The distinguished mathematician E. R. Lorch praised the book in the Bulletin of the American Mathematical Society as “an exposition which is always fresh, proofs which are sophisticated, and a choice of subject matter which is certainly timely.”

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Halmos is back at it again! His concise digestible sections makes it incredibly useful for self study, or small reading groups. While sometimes it is annoying to keep track of the “here on out, this symbol means this”, it’s still a great read. Wonderful exposition.

⭐Visibly, a quite neat and orderly compendium of all basic definitions, theorems and proofs. Hadn’t it been for what I consider to be a misnomer title, evaluation would undoubtedly have been much higher.Now I understand that most european students of unapplied mathematics might enjoy this kind of format, but I myself found the presentation largely unsuitable as introductory material, while I like to think of myself as meeting the prerequisites listed on the first page.Having forced myself through a number of the first sections, I must conclude that there seems to be no hint of historical notice, motivational argument, pedagogical effort, nor any kind of concrete example throughout the book.

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