Fundamentals of the Theory of Operator Algebras. Volume IIAmerican Mathematical Soc., 1997 - 1074 pages This second part of this two-volume work presents 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. Well supplied with exercises, the text assumes only basic measure theory and topology. The books present the possibility for the design of numerous courses aimed at different audiences. |
Table des matières
| 385 | |
| 399 | |
Normal States and Unitary Equivalence | 454 |
The Trace | 504 |
Algebra and Commutant | 584 |
Special Representation of CAlgebras | 711 |
Tensor Products | 800 |
Approximation by Matrix Algebras | 881 |
Crossed Products | 936 |
Direct Integrals and Decompositions | 998 |
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Expressions et termes fréquents
A₁ A₂ abelian abelian projections abelian von Neumann automorphic representation B₁ bounded linear C*-algebra C*-subalgebra central carrier central projection closure commutant convergent Corollary corresponding countably countably decomposable defined dense E₁ element everywhere Exercise F₁ factor of type faithful normal follows H₁ H₂ Hence Hilbert space Hint homomorphism isomorphism L₂(R Lemma linear functional linear mapping linear span matrix units maximal abelian measurable minimal projections modular automorphism group multiplication Neumann algebra acting norm notation null ideal null set orthogonal family p₁ partial isometry polar decomposition positive integer positive linear Proof properly infinite Proposition prove range real number self-adjoint self-adjoint operator separable Hilbert space sequence Show space H strong-operator subalgebra subfactor subprojection subspace Suppose T₁ tensor product Theorem topology tracial weight two-sided ideal ultraweak ultraweakly continuous unique unit ball unit vector unitarily equivalent unitary operator von Neumann algebra weak-operator continuous
Fréquemment cités
Page 393 - Hausdorff spaces X and Y are homeomorphic if and only if C(X) and C(Y) are...
Page 1055 - M. Tomita, Standard forms of von Neumann algebras, Fifth Functional Analysis Symposium of the Math. Soc. of Japan, Sendai, 1967.