Applying projective geometry to transformations on rank one idempotents
Applying projective geometry to transformations on rank one idempotents
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DOI：
10.1016/j.jfa.2003.07.009
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发表时间：
2004-05
影响因子：
1.7
通讯作者：
P. Šemrl
中科院分区：
文献类型：
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作者：
P. Šemrl
给出了Banach空间上所有秩一幂等算子集上双向保持零积的双射变换的Molnár刻画的一个简短证明.给出了对有限维情形的一种改进。应用这些结果刻画了标准算子半群的自同构，并改进了Uhlhorn的Wigner定理。
We present a short proof of Molnár's characterization of bijective transformations on the set of all rank one idempotent operators on a Banach space which preserve zero products in both directions. An improvement in the finite-dimensional case is given. We apply these results to describe automorphisms of standard operator semigroups and to improve Uhlhorn's version of Wigner's theorem.