Derivations on the Banach algebra L1(G) of a locally compact group

In this paper, we present some results concerning derivations and Jordan derivations on the noncommutative Banach algebra L1(G) . We show that the range of any (skew-) centralizing derivation on L1(G) is embedded into M(L1;C(G)), and the zero map is the only skew-commuting derivation on L1(G) . We also prove that the subspace Annr(L1(G) ) of L1(G) is invariant under Jordan derivations

Keywords:

locally compact group , derivation , Jordan derivation , centralizing derivation , skew centralizing derivation .