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The unit ball of the predual of $ H^\infty(\mathbb{B}_d)$ has no extreme points


Authors: Raphaël Clouâtre and Kenneth R. Davidson
Journal: Proc. Amer. Math. Soc. 144 (2016), 1575-1580
MSC (2010): Primary 30H05, 46J15, 47L50
DOI: https://doi.org/10.1090/proc/12964
Published electronically: November 20, 2015
MathSciNet review: 3451234
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Abstract: We identify the exposed points of the unit ball of the dual space of the ball algebra. As a corollary, we show that the predual of $ H^\infty (\mathbb{B}_d)$ has no extreme points in its unit ball.


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Additional Information

Raphaël Clouâtre
Affiliation: Pure Mathematics Department, University of Waterloo, Waterloo, Ontario, Canada
Address at time of publication: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada
Email: raphael.clouatre@umanitoba.ca

Kenneth R. Davidson
Affiliation: Pure Mathematics Department, University of Waterloo, Waterloo, Ontario, Canada
Email: krdavids@uwaterloo.ca

DOI: https://doi.org/10.1090/proc/12964
Keywords: Bounded analytic functions, unit ball, extreme points, predual
Received by editor(s): April 3, 2015
Received by editor(s) in revised form: April 4, 2015
Published electronically: November 20, 2015
Additional Notes: The first author was partially supported by an FQRNT postdoctoral fellowship.
The second author was partially supported by an NSERC grant.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2015 American Mathematical Society