## Amir Sahami

*Generalized notions of amenability for a class of matrix algebras*

Comment.Math.Univ.Carolin. 60,2 (2019) 199-208.**Abstract:**We investigate the amenability and its related homological notions for a class of $I\times I$-upper triangular matrix algebra, say ${\rm UP}(I,A)$, where $A$ is a~Banach algebra equipped with a nonzero character. We show that ${\rm UP}(I,A)$ is pseudo-contractible (amenable) if and only if $I$ is singleton and $A$ is pseudo-contractible (amenable), respectively. We also study pseudo-amenability and approximate biprojectivity of ${\rm UP}(I,A)$.

**Keywords:** upper triangular Banach algebra; amenability; left $\varphi$-amenability; approximate biprojectivity

**DOI:** DOI 10.14712/1213-7243.2019.002

**AMS Subject Classification:** 46M10 43A07 43A20

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