Introduction to Hilbert Space and the Theory of Spectral Multiplicity

by Paul R. Halmos

2013 Reprint of 1951 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. The subject matter of the book is funneled into three chapters: [1] The geometry of Hubert space; [2] the structure of self-adjoint and normal operators; [3] and multiplicity theory for a normal operator. For the last, an expert knowledge of measure theory is indispensable. Indeed, multiplicity theory is a magnificent measure-theoretic tour de force. The subject matter of the first two chapters might be said to constitute an introduction to Hilbert space, and for these, an a priori knowledge of classic measure theory is not essential. Paul Richard Halmos (1916-2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.

Genres: Mathematics, Reference, Textbooks

118 pages, Paperback

First published January 1, 1974

Reviews

[Jay Howard · Rating 3 out of 5]

It has been several years since I've read this book, but I have occasionally returned to it for reference. It is eminently readable, even for someone lacking basically any subject-area knowledge. However, it suffers for the same reason, in that it does not get to any majorly interesting results. It serves exactly as the title says, and no more.