ABSTRACT
Chapter 3
Improvement of Accuracy
Let us rst review the development of the subject matter so far. In
Chapter 1, we have discussed the eigenvalue problem T' = ' for a
bounded operator T on a complex Banach spaceX . In order to obtain an
approximate solution to this problem, in Chapter 2 we have considered
sequences (T
n
) of bounded operators on X which converge to T in an
appropriate manner, and have given error estimates for the solutions of
the approximate eigenvalue problem T
n
'
n
=
n
'
n
.
