A Note on Essentially Left ϕ-Contractible Banach Algebras

In this note, we show that [11, Corollary 3.2] is not always true. In fact, we characterize essential left ϕ-contractibility of group algebras in terms of compactness of its related locally compact group. Also, we show that for any compact commutative group G, L^2(G) is always essentially left ϕ-contractible. We discuss the essential left ϕ-contractibility of some Fourier algebras.