In this paper, we develop greedy algorithms to tackle the problem of finding sparse approximations of zeros of operators in a Hilbert space of possibly infinite dimension. Four greedy algorithms, Subspace Pursuit, CoSaMP, HTP and IHT, which are classically used for sparse approximation, are extended. A criterion, the Restricted Diagonal Property, is developed. It guarantees the definition of the extended algorithms and is used to derive error bounds. We also provide examples and experiments that illustrate these theoretical results.