## Amir Sahami, Mohammad R. Omidi, Eghbal Ghaderi, Hamzeh Zangeneh

*Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras*

Comment.Math.Univ.Carolin. 61,1 (2020) 83-92.**Abstract:**We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a~compact metric space $X$, the Lipschitz algebras ${\rm Lip}_{\alpha}(X)$ and ${\rm lip}_{\alpha}(X)$ are approximately biflat if and only if $X$ is finite, provided that $0<\alpha<1$. We give a~necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat.

**Keywords:** approximate biflatness; Johnson pseudo-contractibility; Lipschitz algebra; triangular Banach algebra

**DOI:** DOI 10.14712/1213-7243.2020.004

**AMS Subject Classification:** 46M10 46H20 46H05

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