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

TL;DR

This paper extends peak set results to non-commutative $H^$-algebras, establishing their unique predual and broadening the applicability of previous theorems in operator algebra theory.

Contribution

It provides a non-commutative version of Amar and Lederer's peak set result and generalizes key properties of non-commutative $H^$-algebras.

Findings

Non-commutative $H^$-algebras have unique preduals

Certain results of Blecher and Labuschagne are now valid in full generality

Extension of peak set theory to non-commutative operator algebras

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.