Theory of Operator Algebras ISince its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects. |
Contents
II | 1 |
III | 2 |
IV | 6 |
V | 13 |
VI | 17 |
VII | 21 |
VIII | 23 |
IX | 25 |
XXIX | 179 |
XXX | 181 |
XXXI | 182 |
XXXII | 188 |
XXXIII | 192 |
XXXIV | 203 |
XXXV | 220 |
XXXVI | 229 |
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A₁ A₂ abelian abelian von Neumann Banach algebra Banach space Borel set Borel space bounded C*-algebra central projection closure commutes completely positive conjugate space continuous function converges strongly convex countable cross-norm cyclic representation define denote dense dµ(v dµ(w e₁ E₂ element enveloping von Neumann equivalent exists f₁ faithful semifinite normal follows Hence Hilbert space homomorphism invariant isometry isomorphism LC(H lower semicontinuous M₁ M₂ maximal abelian measure minimal projection N₁ Neumann algebra norm o-finite o-strong o-strongly operator algebras orthogonal polar decomposition Polish space positive linear functional predual PROOF Q.E.D. Corollary Q.E.D. Definition Q.E.D. Lemma Q.E.D. Proposition Q.E.D. Theorem resp self-adjoint semifinite normal trace sequence Show space H subalgebra Suppose tensor product topology unique unit ball unitary vector von Neumann algebra w₁ x₁