  For testing hypothesis on the covariance operator of functional time series,
we suggest to use the full functional information and to avoid dimension
reduction techniques. The limit distribution follows from the central limit
theorem of the weak convergence of the partial sum process in general Hilbert
space applied to the product space. In order to obtain critical values for
tests, we generalize bootstrap results from the independent to the dependent
case. This results can be applied to covariance operators, autocovariance
operators and cross covariance operators. We discuss one sample and changepoint
tests and give some simulation results.
