Abstract
We study the class of dual operator algebras admitting a normal virtual h-diagonal (i.e. a diagonal in the normal Haagerup tensor product), this property can be seen as a dual operator space version of amenability. After giving several characterizations of these algebras, we show that this class is stable under algebraic perturbations and cb-isomorphisms with small bound. We also prove some perturbation results for the Kadison-Kastler metric.
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