1 results
CO-REPRESENTATIONS OF HOPF–VON NEUMANN ALGEBRAS ON OPERATOR SPACES OTHER THAN COLUMN HILBERT SPACE
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 82 / Issue 2 / October 2010
- Published online by Cambridge University Press:
- 22 June 2010, pp. 205-210
- Print publication:
- October 2010
-
- Article
-
- You have access
- Export citation
-
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.
is a Banach algebra if and only if 𝔐 is subhomogeneous or 