Weakly constricted operators and Jamison’s convergence theorem

Abstract:

If $T$ is a linear contraction on a complex $C(X)$ space which is irreducible and if $\{ {T^n}f\}$ converges weakly to zero then the convergence is actually in norm. If $T$ is weakly constricted and irreducible then $T$ is actually strongly constricted. If $T$ is weakly almost periodic and irreducible and either $T$ or ${T^*}$ has a unimodular point spectral value then $T$ is strongly almost periodic.