LAUSR

Let $$L^{1}(G)$$L1(G) and $$M(G)$$M(G) be the group algebra and the measure algebra of a locally compact group G, respectively, and $$\Delta :L^{1}(G)\rightarrow M(G)$$Δ:L1(G)→M(G) be a continuous linear map. Assuming that $$\Delta $$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 $$\Delta $$Δ is a derivation or anti-derivation through orthogonality conditions on $$L^{1}(G)$$L1(G) such as $$f*g=0$$f∗g=0, $$f*g^{\star }=0$$f∗g⋆=0, $$f^{\star }*g=0$$f⋆∗g=0, $$f*g=g*f=0$$f∗g=g∗f=0 and $$f*g^{\star }=g^{\star }*f=0$$f∗g⋆=g⋆∗f=0.