A new class of ideal Connes amenabilityIn this paper, we introduce a new notion of amenability, $σ-$Connes
ideal, say, for a large class of dual Banach algebras. We extend the concept of
ideal Connes amenability and study their properties. Let $σ$ be a
$weak^{*}$-continuous endomorphism on a dual Banach algebra $\mathcal{A}$ with
dense range. Then the concept of ideal Connes-amenability and $σ-$ ideally
Connes amenability are the same. We gave some general results and hereditary
properties with some examples for this new notion of amenability.
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