Digital Commons Network^™

Bimodules Over Cartan Masas In Von Neumann Algebras, Norming Algebras, And Mercer's Theorem, Jan Cameron, David R. Pitts, Vrej Zarikian

Department of Mathematics: Faculty Publications

In a 1991 paper, R. Mercer asserted that a Cartan bimod- ule isomorphism between Cartan bimodule algebras A1 and A2 extends uniquely to a normal -isomorphism of the von Neumann algebras gener- ated by A1 and A2 (Corollary 4.3 of Mercer, 1991). Mercer's argument relied upon the Spectral Theorem for Bimodules of Muhly, Saito and Solel, 1988 (Theorem 2.5, there). Unfortunately, the arguments in the literature supporting their Theorem 2.5 contain gaps, and hence Mercer's proof is incomplete.

In this paper, we use the outline in Pitts, 2008, Remark 2.17, to give a proof of Mercer's Theorem under the additional …