Maps completely preserving involutions and maps completely preserving Drazin inverse (Q1954354)

Let \(X\) and \(Y\) be real or complex infinite-dimensional Banach spaces and let \(\mathcal A\) and \(\mathcal B\) be standard operator algebras on \(X\) and \(Y\), respectively. In the paper, the authors characterize surjective maps \(\Phi:\mathcal A\to \mathcal B\) that completely preserve involutions in both directions and surjective maps \(\Psi:\mathcal A\to \mathcal B\) that completely preserve the Drazin inverse in both directions.