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Module Connes amenability of hypergroup measure algebras

Massoud Amini — 2015

Open Mathematics

We define the concept of module Connes amenability for dual Banach algebras which are also Banach modules with a compatible action. We distinguish a closed subhypergroup K0 of a locally compact measured hypergroup K, and show that, under different actions, amenability of K, M.K0/-module Connes amenability of M.K/, and existence of a normal M.K0/-module virtual diagonal are related.

Operator Connes-amenability of completely bounded multiplier Banach algebras

Bahman HayatiAbasalt BodaghiMassoud Amini — 2019

Archivum Mathematicum

For a completely contractive Banach algebra B , we find conditions under which the completely bounded multiplier algebra c b ( B ) is a dual Banach algebra and the operator amenability of B is equivalent to the operator Connes-amenability of c b ( B ) . We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.

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