On the Space of Almost Convergent Sequences

The subspace $c_0$ is not complemented in $ac_0$

“…It has turned out that the functional α(x) is closely related to the theory of Banach limits. In particular, the equality A 0 ∩ ac 0 = c 0 holds [10]. In [11] it is shown that T A 0 = A 0 despite the fact that for some x ∈ ℓ ∞ one has α(T x) < α(x).…”