Recent interest in the investigation of chaotic behavior of dynamic systems has led to a broad renewed interest in \(L_1\) Markov operators. The recent monograph of Lasota and Mackey gives a very readable introduction to the methods and applications of this approach to the randomness of deterministic processes. Lasota, Li, and Yorke and Lasota and Yorke have studied the asymptotic periodicity of an \(L_1\) Markov operator which has a constricting set which attracts densities. For strongly constricted systems we obtain asymptotic finite-dimensionality for a contraction on any \(B\)-space. Similar results are obtained for weakly compact constrictors on \(B\)- spaces for which the geometry can be exploited. Bartoszek has extended the strong constrictor results of Lasota, Li and Yorke to positive operators on arbitrary Banach lattices. The approach here has some advantages in that positivity is not required and the \(B\)-space can be arbitrary. Using a clever and elementary argument \textit{J. Komornik} [Tôhoku Math. J., II. Ser. 38, 15-27 (1986; Zbl 0592.47025)] has shown that weak implies strong for a constricted \(L_1\) Markov operator. While the de Leeuw-Glicksberg machinery we bring to bear does give some results in an effortless fashion, it does not give this result. We give an example of a positive isometry of \(C(X)\) which is weakly but not strongly constricted to show that a full strength Komornik Theorem is not possible in \(C(X)\).