Abstract:We study the notion of left $\varphi$-biflatness for Segal algebras and semigroup algebras. We show that the Segal algebra $S(G)$ is left $\varphi$-biflat if and only if $G$ is amenable. Also we characterize left $\varphi$-biflatness of semigroup algebra $l^{1}(S)$ in terms of biflatness, when $S$ is a Clifford semigroup.
Keywords: left $\varphi$-biflat; Segal algebra; semigroup algebra; locally compact group
DOI: DOI 10.14712/1213-7243.2020.027
AMS Subject Classification: 46M10 43A07 43A20