Introduction to Hilbert space: And the theory of spectral multiplicity

by Paul R. Halmos, Sterling K. Berberian

Halmos, Paul R. Introduction to Hilbert Space and the Theory of Spectral Multiplicity. First Edition. New York, Chelsea Publishing Company, 1951. 23.5cm x 15.4cm. 114 pages. Original Hardcover. Gilt lettering on spine. Very good condition with only minor signs of wear. Titlepage signed by preowner. Includes for Linear funtionals/ Bilinear functionals/ Quadratic forms/ Inner product and Norm/ The inequalities of Bessel and Schwartz/ Infinate sums/ Conditions for summability/ Examples of Hilbert Spaces/ Subspaces/ Vectors in and out of Subspaces/ Orthogonal complements/ Vector sums/ Bases/ A non-closed vector sum/ Dimension/ Boundedness/ Bounded Bilinear functionals/ The algebra of operators/ Operators/ Examples of operators/ Inverses/ Adjoints/ Invariance/ Hermitian operators/ Normal and unitary operators/ Projections/ Infima and suprema of projections/ The spectrum of an operator/ Compactness of Spectra/ Transforms of Spectra/ Spectral heuristics/ Spectral measures/ Spectral integrals/ Regular spectral measures/ Real and complex spectral measures/ Description of the spectral subspaces/ The spectral theorem for Hermitian Operators/ The analysis of spectral measures/ The problem of Unitary Equivalence/ Multiplicity functions in finite-dimensional spaces/ Measures/ Boolean operations on measures/ Multiplicity functions/ The canonical example of a spectral measure/ The commutator of a set of projections/ Pairs of commutators/ Columns/ rows/ cycles/ Separable projections/ Characterizations of rows/ Cycles and rows/ The existence of rows/ Orthogonal systems/ The power of a Maximal Orthogonal System/ Multiplicities/ Measures from vectors/ subspaces from measures/ The multiplicity function of a spectral measure etc.

Genres: Mathematics, Reference, Textbooks

114 pages, Hardcover

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.