Preduals of $H^{\infty }$ of finitely connected domains
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- by Mohan Ravichandran and Onur Yavuz PDF
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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.References
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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
- 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
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3168470