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Maps completely preserving idempotents and maps completely preserving square-zero operators. (English) Zbl 1189.47035
Summary: Let X,Y be real or complex Banach spaces with dimension greater than 2 and let 𝒜, be standard operator algebras on X and Y, respectively. In this paper, we show that every map completely preserving idempotence from 𝒜 onto is either an isomorphism or (in the complex case) a conjugate isomorphism; every map completely preserving square-zero from 𝒜 onto is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism.
MSC:
47B49Transformers, preservers (operators on spaces of operators)
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