  In this article, we consider the linear operator equation in a Banach space.
The relative perturbation of the solution x corresponding to the perturbation
of y, the perturbation of A and the perturbation of both A, y are characterized
from the pseudospectrum and the condition pseudospectrum of A. Certain examples
are given to illustrate the results. A relation between the pseudospectrum and
the condition pseudospectrum of an operator are established. The distance to
instability and the distance to singularity of an operator are also found from
the condition pseudospectrum of the operator.

Spectral Theory