Additive Jordan derivations of reflexive algebras (Q868769)

Let \(\mathcal{L}\) be a subspace lattice on a Banach space \(X\) such that either \((0)_{+} \neq (0)\) or \(X_{-}\neq X\), and let \(A\) be a standard subalgebra of \(\text{Alg}\mathcal L\). It is shown that every additive Jordan derivation \(\delta:A\to B(X)\) is an additive derivation. If \(\mathcal L = \mathcal N\) is a nest, then the assumption that \((0)_+\neq (0)\) or \(X_-\neq X\) can be omitted.