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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 $𝒜,ℬ$ be standard operator algebras on $X$ and $Y$, respectively. In this paper, we show that every map completely preserving idempotence from $𝒜$ onto $ℬ$ is either an isomorphism or (in the complex case) a conjugate isomorphism; every map completely preserving square-zero from $𝒜$ onto $ℬ$ is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism.
##### MSC:
 47B49 Transformers, preservers (operators on spaces of operators)
##### Keywords:
idempotence preserving maps
##### References:
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