Maps completely preserving spectral functions

Let X,Y be infinite dimensional complex Banach spaces and A,B be standard operator algebras on X and Y, respectively. In this paper, we show that surjective maps completely preserving certain spectral function Δ(·) from A to B are isomorphisms, where Δ(·) stands for any one of 13 spectral functions σ(·), σl(·), σr(·), σl(·)∩σr(·), ∂σ(·), ησ(·), σp(·), σc(·), σp(·)∩σc(·), σp(·)∪σc(·), σap(·), σs(·), and σap(·)∩σs(·).