The unit ball of the predual of $H^\infty(\mathbb{B}_d)$ has no extreme points
@article{Clouatre2015TheUB, title={The unit ball of the predual of \$H^\infty(\mathbb\{B\}\_d)\$ has no extreme points}, author={Raphael Clouatre and Kenneth R. Davidson}, journal={arXiv: Functional Analysis}, year={2015} }
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.
2 Citations
Non‐commutative peaking phenomena and a local version of the hyperrigidity conjecture
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- 2017
We investigate various notions of peaking behaviour for states on a C∗ ‐algebra, where the peaking occurs within an operator system. We pay particularly close attention to the existence of sequences…
References
SHOWING 1-10 OF 18 REFERENCES
Function Theory in the Unit Ball of Cn
- Mathematics
- 1980
Preliminaries.- The Automorphisms of B.- Integral Representations.- The Invariant Laplacian.- Boundary Behavior of Poisson Integrals.- Boundary Behavior of Cauchy Integrals.- Some Lp-Topics.-…
Operator Algebras with Unique Preduals
- MathematicsCanadian Mathematical Bulletin
- 2011
Abstract We show that every free semigroup algebra has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak- $*$ closed unital operator algebra containing a weak-…
A non-self-adjoint Lebesgue decomposition
- Mathematics
- 2013
We study the structure of bounded linear functionals on a class of non-self-adjoint operator algebras that includes the multiplier algebra of every complete Nevanlinna-Pick space, and in particular…
A Course in Functional Analysis
- Education
- 1985
This book is an introductory text in functional analysis, aimed at the graduate student with a firm background in integration and measure theory. Unlike many modern treatments, this book begins with…
Accessible points of a functional compact set (Russian)
- Doklady Akad. Nauk. SSSR (N.S.)
- 1948
A course in functional analysis, 2nd
- ed., Graduate Texts in Math. 96,
- 1990
On the predual of H∞
- Comment. Math. Special Issue
- 1978