Classification of W*-Algebras
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Let p, q be two projections of a W*-algebra M. If there exists a partial isometry u in M such that u*u = p and uu* = q, then p is said to be equivalent to q and denote this by p~q. If there exists a projection q1 (≤q) equivalent to p, we write this by p<q or q>p. We write p~q or p<q by p≤q.
KeywordsHilbert Space Coupling Function Central Projection Partial Isometry Closed Linear Operator
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