In this presentation, we present a four-step procedure to test the equality of two covariance operators in functional data samples. This method covers the situation where partial functional data are fully observed on dense lattice and other partial are incompletely observed, as well as the case where the recordings of all of curves are available on a regular and dense grid. The procedure leads to a global testing statistic. In the procedure, we obtain projected covariance operators based on an initial functional principal component analysis and then form a global test statistic based on the projected covariance operators and their corresponding variance estimates. The asymptotic properties of the test statistic are presented. Simulation results demonstrate that the test controls Type I error rates at a reasonable level and may provide superior power results compared with the existing methods. We show a real life application of the proposed test involving air pollution data to test whether there are conjectured differences of volatility in air pollution between working days and non-working days, and between seasons.