Equivalence of projections

Berberian, S. K.

doi:10.1090/S0002-9939-1972-0295090-6

Equivalence of projections
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by S. K. Berberian PDF

Proc. Amer. Math. Soc. 33 (1972), 485-490 Request permission

Abstract:

Theorem: An $A{W^\ast }$-algebra is the ring generated by its projections if and only if it has no abelian summand. Corollary: Every equivalence in an $A{W^\ast }$-algebra may be implemented by a partial isometry in the ring generated by the projections of the algebra. The corollary is extended to certain finite Baer $\ast$-rings.

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