Preduals of 𝐻^{∞} of finitely connected domains

Ravichandran, Mohan; Yavuz, Onur

doi:10.1090/S0002-9939-2014-11927-7

Preduals of $H^{\infty }$ of finitely connected domains
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by Mohan Ravichandran and Onur Yavuz PDF

Proc. Amer. Math. Soc. 142 (2014), 1641-1648 Request permission

Abstract:

A well known result of Ando says that $H^{\infty }(\mathbb {D})$ has a unique predual. There have been two natural extensions of this result to non-commutative algebras: Ueda showed that finite maximal subdiagonal algebras have unique preduals. In a second direction, Davidson and Wright showed that free semi-group algebras have unique preduals. In these notes, we explore a different natural generalization of this result: Let $A$ be a finitely connected domain in the plane. We show that $H^{\infty }(A)$ has a unique isometric predual. We also prove a couple of theorems about the structure of the unique predual.

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