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Review: Fundamentals of the Theory of Operator Algebras (Graduate Studies in Mathematics, V. 15) (Graduate Studies in Mathematics, V. 15)User Review - Mataiga - Goodreads
I learned more about self adjoint operator and v Neumann algebras Read full review
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abelian abelian projections abelian von Neumann automorphic representation automorphism group bounded linear operator C*-algebra C*-subalgebra center-valued trace central carrier central projection commutant compact contains Corollary corresponding countably 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 weak-operator continuous
Page 1053 - M. Tomita, Standard forms of von Neumann algebras, Fifth Functional Analysis Symposium of the Math. Soc. of Japan, Sendai, 1967.
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