  This paper deals with analyzing structural breaks in the covariance operator
of sequentially observed functional data. For this purpose, procedures are
developed to segment an observed stretch of curves into periods for which
second-order stationarity may be reasonably assumed. The proposed methods are
based on measuring the fluctuations of sample eigenvalues, either individually
or jointly, and traces of the sample covariance operator computed from segments
of the data. To implement the tests, new limit results are introduced that deal
with the large-sample behavior of vector-valued processes built from partial
sample eigenvalue estimates. These results in turn enable the calibration of
the tests to a prescribed asymptotic level. A simulation study and an
application to Australian annual minimum temperature curves confirm that the
proposed methods work well in finite samples. The application suggests that the
variation in annual minimum temperature underwent a structural break in the
1950s, after which typical fluctuations from the generally increasing
trendstarted to be significantly smaller.
