Let A and B be standard operator algebras on Banach spaces X and Y , respectively. In this paper, we show that every map completely preserving fixed points property from A onto B is either an isomorphism or (in the complex case) a conjugate isomorphism. Also we show that every map completely preserving kernel of operators from A onto B is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism. B be standard operator algebras on Banach spaces X and Y , respectively. In this paper, we show that every map completely preserving the fixed points property from A onto B is either an isomorphism or (in the complex case) a conjugate isomorphism. Also we show that every map completely preserving the kernel of operators from A onto B is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism.
