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CO-REPRESENTATIONS OF HOPF–VON NEUMANN ALGEBRAS ON OPERATOR SPACES OTHER THAN COLUMN HILBERT SPACE
Published online by Cambridge University Press: 22 June 2010
Abstract
Recently, Daws introduced a notion of co-representation of abelian Hopf–von Neumann algebras on general reflexive Banach spaces. In this note, we show that this notion cannot be extended beyond subhomogeneous Hopf–von Neumann algebras. The key is our observation that, for a von Neumann algebra 𝔐 and a reflexive operator space E, the normal spatial tensor product is a Banach algebra if and only if 𝔐 is subhomogeneous or E is completely isomorphic to column Hilbert space.
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- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 82 , Issue 2 , October 2010 , pp. 205 - 210
- Copyright
- Copyright © Australian Mathematical Publishing Association Inc. 2010
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