Fundamentals of the Theory of Operator Algebras. Volume II

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American Mathematical Soc., 1997 - Mathematics - 1074 pages
From the reviews for Volumes I and II: ... these two volumes represent a magnificent achievement. They will be an essential item on every operator algebraist's bookshelves and will surely become the primary source of instruction for research students in von Neumann algebra theory. --Bulletin of the London Mathematical Society This book is extremely clear and well written and ideally suited for an introductory course on the subject or for a student who wishes to learn the fundamentals of the classical theory of operator algebras. --Zentralblatt MATH This work and Fundamentals of the Theory of Operator Algebras. Volume I, Elementary Theory (Graduate Studies in Mathematics, Volume 15) present an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Major concepts are sometimes presented from several points of view; the account is leisurely when brevity would compromise clarity. An unusual feature in a text at this level is the extent to which it is self-contained; for example, it introduces all the elementary functional analysis needed. The emphasis is on teaching. Well supplied with exercises, the text assumes only basic measure theory and topology. The book presents the possibility for the design of numerous courses aimed at different audiences.

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Comparison Theory of Projection
Normal States and Unitary Equivalence
Linear Spaces
The Trace
Algebra and Commutant
Basics of Hilbert Space and Linear Operators
Special Representation of CAlgebras
Elementary CAIgebra Theory
Approximation by Matrix Algebras
Crossed Products
Elementary von Neumann Algebra Theory
Direct Integrals and Decompositions
Banach Algebras

Tensor Products

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Page xv - Hausdorff spaces X and Y are homeomorphic if and only if C(X) and C(Y) are...
Page 1053 - M. Tomita, Standard forms of von Neumann algebras, Fifth Functional Analysis Symposium of the Math. Soc. of Japan, Sendai, 1967.
Page 1053 - A proof of Tomita's fundamental theorem in the theory of standard von Neumann algebras".
Page 1049 - W. Rudin, Real and complex analysis, 2nd ed., McGraw-Hill, New York, 1974.

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