For a sequence \(x=(x_n)\) put \(\Delta x = (x_1-x_2, x_2-x_3, \ldots)\); \(\Delta^n x = \Delta \Delta^{n-1}x\). For a sequence space \(X\) the authors define the sequence space generated by the operator \(\Delta^n\) : \(\Delta^n(X) = \{x=(x_n): \Delta^n x \in X\}\). The properties of \(\Delta^n(X)\) are studied for general \(X\) and for two closely related examples of spaces \(X\): for the space of sequences, convergent in the sense of \(p\)-means; and for the space of statistically convergent sequences.