Let \(\mathcal {A}\) be a \(C^{*}\) -algebra acting on a Hilbert space H. We prove that every antiderivation from \(\mathcal {A}\) into B(H) is inner. If \(\mathcal {N}\) is a nest of subspaces of H with \(dim(H)>1\) , then there exists a nonzero antiderivation on the nest algebra \(\mathcal {T}(\mathcal {N})\) if and only if \(dim((0)_{+})=dim(H \ominus H_{-})=1.\) Let \(\mathcal {A}\) be a semiprime Banach algebra with a semisimple center. Then every bounded antiderivation on \(\mathcal {A}\) is zero. Finally, if \(\mathcal {A}\) is a semisimple Banach algebra with a nonzero socle, there are no nonzero antiderivations from the socle into \(\mathcal {A}.\)
