This is an announcement for the paper "Characterizing arbitrarily slow convergence in the method of alternating projections" by H.H. Bauschke, F. Deutsch and H. Hundal. Abstract: In 1997, Bauschke, Borwein, and Lewis have stated a trichotomy theorem that characterizes when the convergence of the method of alternating projections can be arbitrarily slow. However, there are two errors in their proof of this theorem. In this note, we show that although one of the errors is critical, the theorem itself is correct. We give a different proof that uses the multiplicative form of the spectral theorem, and the theorem holds in any real or complex Hilbert space, not just in a real Hilbert space. Archive classification: math.FA math.OC Mathematics Subject Classification: 47B20 The source file(s), 071010.tex: 35102 bytes, is(are) stored in gzipped form as 0710.2387.gz with size 12kb. The corresponding postcript file has gzipped size 96kb. Submitted from: heinz.bauschke@ubc.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0710.2387 or http://arXiv.org/abs/0710.2387 or by email in unzipped form by transmitting an empty message with subject line uget 0710.2387 or in gzipped form by using subject line get 0710.2387 to: math@arXiv.org.