Abstract
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.
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© 1998 Springer-Verlag Berlin Heidelberg
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Sakai, S. (1998). Classification of W*-Algebras. In: C*-Algebras and W*-Algebras. Classics in Mathematics, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61993-9_2
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DOI: https://doi.org/10.1007/978-3-642-61993-9_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63633-5
Online ISBN: 978-3-642-61993-9
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