# Maps completely preserving idempotents and maps completely preserving square-zero operators

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DOI: 10.1007/s11856-010-0032-y

- Cite this article as:
- Hou, J. & Huang, L. Isr. J. Math. (2010) 176: 363. doi:10.1007/s11856-010-0032-y

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## Abstract

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.

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© Hebrew University Magnes Press 2010