Naj bo ▫$X$▫ neskončno dimenzionalen Banachov prostor in naj bo ▫$\Phi : B(X)\to B(X)$▫ surjektivna linearna preslikava z lastnostjo ▫$\Phi (I)=I$▫. Če ▫$\Phi$▫ ohranja injektivne operatorje v obeh ...smereh, potem je ▫$\Phi$▫ avtomorfizem algebre ▫$B(X)$▫. Naj bo ▫$X$▫ Hilbertov prostor. Potem je ▫$\Phi$▫ avtomorfizem natanko tedaj, ko ▫$\Phi$▫ ohranja surjektivne operatorje v obeh smereh.
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