Maps completely preserving idempotents and maps completely preserving square-zero operators
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- Hou, J. & Huang, L. Isr. J. Math. (2010) 176: 363. doi:10.1007/s11856-010-0032-y
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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.