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∞-algebra H∞(M,τ) has unique predual,and moreover some
restriction in some of the results of Blecher and Labuschagne are removed,
making them hold in full generality.Comment: final version (the presentation of some part is revised and one
reference added