Let L^1(G) and M(G) be the group algebra and the measure algebra of a locally compact group G, respectively, and Δ : L1(G) →M(G) be a continuous linear map. Assuming that Δ behaves like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions, our aim is to characterize such maps. Indeed, we assume that Δ is a derivation or anti-derivation through orthogonality conditions on L^1(G) such as f ∗ g = 0, f ∗ g* = 0, f * ∗ g = 0, f ∗ g = g ∗ f = 0 and f ∗ g* = g*∗ f = 0.
