Jordan triple derivations on J-subspace lattice algebras

Let L be a J-subspace lattice on a Banach space X and AlgL the associated J-subspace lattice algebra. Let A be a standard operator subalgebra (i.e., it contains all finite rank operators in AlgL) of AlgL and M . B(X) the AlgL-bimodule. It is shown that every linear Jordan triple derivation from A into M is a derivation, and that every generalized Jordan (triple) derivation from A into M is a generalized derivation.