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