Maps completely preserving fixed points and maps completely preserving kernel of operators (Q1715041)

The authors characterize the forms of maps that completely preserve the fixed point property and completely preserve the kernel of operators between standard operator algebras. For example, let $A$ and $B$ be standard operator algebras on Banach spaces $X$ and $Y$, respectively. Here, they show that every map completely preserving the fixed point property from $A$ onto $B$ is either an isomorphism or a conjugate isomorphism (in the complex case).