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Keywords:
amenability; Connes-amenability; dual multiplier algebra; normal virtual operator diagonal
amenability; Connes-amenability; dual multiplier algebra; normal virtual operator diagonal
Summary:
For a completely contractive Banach algebra $B$, we find conditions under which the completely bounded multiplier algebra $\mathcal{M}_{cb}(B)$ is a dual Banach algebra and the operator amenability of $B$ is equivalent to the operator Connes-amenability of $\mathcal{M}_{cb}(B)$. We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.
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