Fundamentals of the Theory of Operator Algebras. Volume II
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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abelian abelian projections abelian von Neumann automorphic representation bounded linear operator C*-algebra C*-subalgebra center-valued trace central carrier central projection commutant compact contains Corollary corresponding countably decomposable Deduce denote direct sum equation everywhere factor of type faithful normal finite von Neumann follows g in G GNS construction Hence Hilbert space Jf Hint homomorphism irreducible representations isomorphism Lemma linear operator linear span matrix units maximal abelian measure minimal projections modular automorphism group modular condition Moreover multiplicity Neumann algebra acting non-zero projection norm-closed normal semi-finite null set orthogonal family partial isometry polar decomposition positive integer Proof properly infinite Proposition prove quasi-equivalent range real number representation of 21 result satisfies Section self-adjoint operator separable Hilbert space separating vector Show subalgebra subprojection subspace tensor product Theorem topology two-sided ideal ultraweak unique unit ball unit vector unitarily equivalent unitary operator universal representation von Neumann algebra weak-operator continuous
Page xv - Hausdorff spaces X and Y are homeomorphic if and only if C(X) and C(Y) are...
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