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Preduals of $ H^{\infty}$ of finitely connected domains


Authors: Mohan Ravichandran and Onur Yavuz
Journal: Proc. Amer. Math. Soc. 142 (2014), 1641-1648
MSC (2010): Primary 46J15; Secondary 46E15
DOI: https://doi.org/10.1090/S0002-9939-2014-11927-7
Published electronically: February 13, 2014
MathSciNet review: 3168470
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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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Additional Information

Mohan Ravichandran
Affiliation: Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, 34956, Istanbul, Turkey

Onur Yavuz
Affiliation: Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, 34956, Istanbul, Turkey
Address at time of publication: Department of Science and Mathematics, Columbia College, 623 S. Wabash Avenue, Chicago, Illinois 60605
Email: oyavuz-geckil@colum.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11927-7
Received by editor(s): March 26, 2012
Received by editor(s) in revised form: June 5, 2012
Published electronically: February 13, 2014
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society