  An extension of Chernoff's product formula for one-parameter functions taking
values in the space of bounded linear operators on a Banach space is given.
Essentially, the $n$-th one-parameter function in the product formula is mapped
by the $n$-th iterate of a contraction acting on the space of the one-parameter
functions. The motivation to study this specific product formula lies in the
growing field of dynamical control of quantum systems, involving the procedure
of dynamical decoupling and also the Quantum Zeno effect.
