On the predual of non-commutative $H^\infty$

TL;DR

This paper investigates the unique predual of non-commutative H-infinity algebras, focusing on the liftability of weakly relatively compact subsets, advancing understanding of their dual space structure.

Contribution

It proves the liftability property of weakly relatively compact subsets in the predual of non-commutative H-infinity algebras, a novel result in the field.

Findings

Established liftability of weakly relatively compact subsets

Enhanced understanding of the predual structure of non-commutative H-infinity

Contributed to the theory of non-commutative function spaces

Abstract

The unique predual $M_\star/A_\perp$ of a non-commutative $H^\infty$-algebra $A = H^\infty(M,\tau)$ is investigated. In particular, we will prove the liftability property of weakly relatively compact subsets in $M_\star/A_\perp$ to $M_\star$.