Abstract
In this paper, we introduce and study the notion of left [Formula: see text]-essential Connes amenable for dual Banach algebras. We investigate the hereditary properties of this new concept and we give some results for [Formula: see text]-Lau product and module extension. For unital dual Banach algebras, we show that left [Formula: see text]-essential Connes-amenability and left [Formula: see text]-Connes amenability are equivalent. Finally, with various examples, we examined this concept for upper triangular matrix algebras and [Formula: see text]-direct sum of Banach algebras.
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