  In this paper, we study the notion of Johnson pseudo-contractibility for
certain Banach algebras. For a bicyclic semigroup $S$, we show that
$\ell^{1}(S)$ is not Johnson pseudo-contractible. Also for a Johnson
pseudo-contractible Banach algebra $A$, we show that $A$ has no non-zero
complemented closed nilpotent ideal.
