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Statistical methods for functional data are of interest for manyapplications. In this paper, we prove a central limit theorem for randomvariables taking their values in a Hilbert space. The random variables areassumed to be weakly dependent in the sense of near epoch dependence, where theunderlying process fulfills some mixing conditions. As parametric inference inan infinite dimensional space is difficult, we show that the nonoverlappingblock bootstrap is consistent. Furthermore, we show how these results can beused for degenerate von Mises-statistics.

Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics