Document Type
Article
Publication Date
Spring 1990
Abstract
Given a Cartan subalgebra A of a non Neumann algebra M, the techniques of Feldman and Moore are used to analyze the partial isometries v in M such that v* Av is contained in A. Orthonormal bases for M consisting of such partial isometries are discussed, and convergence of the resulting generalized fourier series is shown to take place in the Bures A-topology. The Bures A-topology is shown to be equivalent to the strong topology on the unit ball of M. These ideas are applied to A-bimodules and to give a simplified and intuitive proof of the Spectral Theorem for Bimodules first proven by Muhly, Saito, and Solel.
Repository Citation
Mercer, R.
(1990). Bimodules Over Cartan Subalgebras. Rocky Mountain Journal of Mathematics, 20 (2), 487-502.
https://corescholar.libraries.wright.edu/math/34
DOI
10.1216/rmjm/1181073123
