On peak phenomena for non-commutative $H^{\infty }$

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 restriction in some of the results of Blecher and Labuschagne are removed, making them hold in full generality.

final version (the presentation of some part is revised and one reference added)

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