  In this paper we propose statistical inference tools for the covariance
operators of functional time series in the two sample and change point problem.
In contrast to most of the literature the focus of our approach is not testing
the null hypothesis of exact equality of the covariance operators. Instead we
propose to formulate the null hypotheses in them form that "the distance
between the operators is small", where we measure deviations by the sup-norm.
We provide powerful bootstrap tests for these type of hypotheses, investigate
their asymptotic properties and study their finite sample properties by means
of a simulation study.
