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MORE ON THE ARENS REGULARITY OF
$B(X)$
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 94 / Issue 2 / October 2016
- Published online by Cambridge University Press:
- 01 March 2016, pp. 296-303
- Print publication:
- October 2016
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- Article
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We focus on a question raised by Daws [‘Arens regularity of the algebra of operators on a Banach space’, Bull. Lond. Math. Soc.36 (2004), 493–503] concerning the Arens regularity of
$B(X)$, the algebra of operators on a Banach space 
$X$. Among other things, we show that 
$B(X)$ is Arens regular if and only if 
$X$ is ultrareflexive.
Operator Algebras with Unique Preduals
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- Journal:
- Canadian Mathematical Bulletin / Volume 54 / Issue 3 / 01 September 2011
- Published online by Cambridge University Press:
- 20 November 2018, pp. 411-421
- Print publication:
- 01 September 2011
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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.
THE OPERATOR HILBERT SPACE OH AND TYPE III VON NEUMANN ALGEBRAS
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- Journal:
- Bulletin of the London Mathematical Society / Volume 36 / Issue 4 / July 2004
- Published online by Cambridge University Press:
- 14 June 2004, pp. 455-459
- Print publication:
- July 2004
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