  For a discrete dynamics defined by a sequence of bounded and not necessarily
invertible linear operators, we give a complete characterization of exponential
stability in terms of invertibility of a certain operator acting on suitable
Banach sequence spaces. We connect the invertibility of this operator to the
existence of a particular type of admissible exponents. For the bounded orbits,
exponential stability results from a spectral property. Some adequate examples
are presented to emphasize some significant qualitative differences between
uniform and nonuniform behavior.
