Introduction to Operator Algebras
This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students.
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The Classification of Von Neumann Algebras
a-finite abelian abelian projection algebra on H assume automorphism group Banach space Borel map Borel measure Borel space Borel subset bounded C*-algebra C*-norm C*-subalgebra Clearly closed subset closed two-sided ideal compact subset contradiction countable define denoted equivalent exists finite projection follows Further Hence Hilbert space irreducible isometry isomorphic Let G linear subspace maximal measurable field Moreover non-zero central projection non-zero projection nondegenerate norm open subset orthogonal family Pick polar decomposition Polish space positive linear functional projection from H Proof properly infinite purely infinite Q.E.D. Definition Q.E.D. Lemma Q.E.D. Proposition Q.E.D. Theorem regular Borel measure representation respectively semi-finite normal trace sequence space H spectral space strongly continuous subalgebra subfactor suffices to show supp Suppose topology trace on M+ uniquely extended unit ball unitary element unitary operator VN algebra xa G Zorn lemma
The Complete Dimension Theory of Partially Ordered Systems with ..., Issue 831
K. R. Goodearl,Friedrich Wehrung
No preview available - 2005