Abstract
Throughout this section, A is a Baer ∗-ring (satisfying various axioms as needed). We assume given a pair of equipotent families of projections (eı)ı∈I, (fı)ı∈I such that (i) the eı, are orthogonal, (ii) the fı are orthogonal, and (iii) eı∼fı for all ı∈I. We write
Thus, \((e_{\i})_{_{\i\in I}}\), (fı)ı∈I are equivalent partitions of e, f [§17, Def. 1]. For each ı∈I, we denote by wı, a fixed partial isometry such that \(w^{*}_{\i}w_{\i}=e_{\i}\), \(w_{\i}w^{*}_{\i}=f_{\i}\).
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© 1972 Springer-Verlag Berlin Heidelberg
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Berberian, S.K. (1972). Additivity of Equivalence. In: Baer ∗-Rings. Grundlehren der mathematischen Wissenschaften, vol 195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15071-5_4
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DOI: https://doi.org/10.1007/978-3-642-15071-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-05751-2
Online ISBN: 978-3-642-15071-5
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