  We investigate the discrete-time quantum walk evolution under the influence
of the periodic measurements in position subspace. The undisturbed survival
probability of the particle at the position subspace, $P(0, t)$ is compared
with the survival probability after frequent ($n$) measurements at interval
$\tau = t/n$, $P(0, \tau)^n$. We show that $P(0, \tau)^n > P(0, t)$ leading to
the quantum Zeno effect in the position subspace when a parameter $\theta$ in
the quantum coin operations and frequency of measurements is greater than the
critical value, $\theta > \theta_{c}$ and $n>n_{c}$. This Zeno effect in the
subspace preserves the dynamics in coin Hilbert space of the walk dynamics and
has a potential to play a significant role in quantum tasks such as, preserving
the quantum state of the particle at any particular position and to understand
the Zeno dynamics in a multidimensional system which is highly transient in
nature.
