Additive maps on standard operator algebras preserving parts of the spectrum ✩,✩✩

Let A and B be standard operator algebras on infinite dimensional complex Banach spaces X and Y, respectively, and let Φ be a unital additive surjection from A onto B. We introduce thirteen parts of the spectrum for elements in A and B, and prove that if Φ preserves any one of these parts of the spectrum, then it is either an isomorphism or an anti-isomorphism.  2003 Elsevier Science (USA). All rights reserved