# Operator Algebras with Unique Preduals

@article{Davidson2011OperatorAW, title={Operator Algebras with Unique Preduals}, author={Kenneth R. Davidson and Alex Wright}, journal={Canadian Mathematical Bulletin}, year={2011}, volume={54}, pages={411 - 421} }

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- $*$ dense subalgebra of compact operators has a unique Banach space predual.

## 9 Citations

Uniqueness of Preduals in Spaces of Operators

- MathematicsCanadian Mathematical Bulletin
- 2014

Abstract We show that if $E$ is a separable reflexive space, and $L$ is a weak-star closed linear subspace of $L\left( E \right)$ such that $L\cap K\left( E \right)$ is weak-star dense in $L$ , then…

Preduals of ^{∞} of finitely connected domains

- Mathematics
- 2014

A well known result of Ando says that H∞(D) has a unique predual. There have been two natural extensions of this result to non-commutative algebras: Ueda showed that finite maximal subdiagonal…

Lebesgue decomposition of functionals and unique preduals for commutants modulo normed ideals

- Mathematics
- 2016

We prove an analogue of the Lebesgue decomposition for continuous functionals on the commutant modulo a reflexive normed ideal of an n-tuple of hermitian operators for which there are quasicentral…

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…

Analytic Free Semigroup Algebras and Hopf Algebras

- Mathematics
- 2012

Let $\fS$ be an analytic free semigroup algebra. In this paper, we explore richer structures of $\fS$ and its predual $\fS_*$. We prove that $\fS$ and $\fS_*$ both are Hopf algebras. Moreover, the…

THE UNIT BALL OF THE PREDUAL OF H ∞ ( B d ) HAS NO EXTREME POINTS

- Mathematics
- 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(Bd) has no extreme points in its unit ball.

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

- Mathematics
- 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.

Erratum to: The algebraic structure of non-commutative analytic Toeplitz algebras

- Mathematics
- 2015

The algebraic structure of the non-commutative analytic Toeplitz algebra Ln is developed in the original article. Some of the results fail for the case n = ∞, and this implies that certain other…

Two-phase problems with distributed sources: regularity of the free boundary

- Mathematics
- 2014

We investigate the regularity of the free boundary for a general class of two-phase free boundary problems with non-zero right hand side. We prove that Lipschitz or flat free boundaries are…

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