This is an announcement for the paper "On peak phenomena for non-commutative $H^\infty$" by Yoshimichi Ueda. Abstract: A non-commutative extension of Amar and Lederer's peak set result is given. As its simple applications it is shown that any non-commutative $H^\infty$-algebra $H^\infty(M,\tau)$ has unique predual, and moreover some of the results of Blecher and Labuschagne are generalized to the complete form. Archive classification: math.FA math.OA The source file(s), peak.tex: 31983 bytes, is(are) stored in gzipped form as 0802.3449.gz with size 10kb. The corresponding postcript file has gzipped size 78kb. Submitted from: ueda@math.kyushu-u.ac.jp The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3449 or http://arXiv.org/abs/0802.3449 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3449 or in gzipped form by using subject line get 0802.3449 to: math@arXiv.org.