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DEFIniTION AND BASIC PROPERTIES
ELEMENTARY OPERATIONS ON VON NEUMANN
27 other sections not shown
a-finite abelian von Neumann algebra in H antiisomorphic automorphism C*-algebra canonical central support centre chapter commutes complex Hilbert space continuous linear form converges strongly corollary countable cyclic decomposable defined denote discrete disjoint projections elements of H equivalent everywhere exercise factor of type faithful normal trace finite factor finite projection finite resp finite von Neumann function fundamental projection Gelfand isomorphism hence hermitian Hilbert algebra homomorphism lemma Let H linear mapping linear subspace locally compact space Math maximal measurable field measurable vector fields Moreover necessary and sufficient negligible set Neumann algebra non-zero projection normal positive linear pairwise disjoint partial isometry polar decomposition positive linear form possessing the following projection F Proof properly infinite purely infinite scalar Show space H subset Suppose supremum theorem tion trace on A+ two-sided ideal ultra-strong ultra-weakly continuous unit ball unitary operator V-measurable weak topology whence Z-trace