Maps completely preserving commutativity and maps completely preserving Jordan zero-product

Let X, Y be real or complex Banach spaces with infinite dimension, and let A, B be standard operator algebras on X and Y, respectively. In this paper, we show that every map completely preserving commutativity from A onto B is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism. Every map completely preserving Jordan zero-product from A onto B is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism.