Operator Connes-amenability of completely bounded multiplier Banach algebras

Bahman Hayati, Abasalt Bodaghi, and Massoud Amini

Address:
Department of Mathematics, Malayer University, Malayer, Hamedan, Iran
Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran
Department of Mathematics, Tarbiat Modares University, P.O.Box 14115-134, Tehran, Iran

E-mail:
hayati@malayeru.ac.ir
abasalt.bodaghi@gmail.com
mamini@modares.ac.ir

Abstract: 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.

AMSclassification: primary 46H20.

Keywords: amenability, Connes-amenability, dual multiplier algebra, normal virtual operator diagonal.

DOI: 10.5817/AM2019-1-31