Applying projective geometry to transformations on rank one idempotents (Q1876271)
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scientific article; zbMATH DE number 2091746
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Applying projective geometry to transformations on rank one idempotents |
scientific article; zbMATH DE number 2091746 |
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Applying projective geometry to transformations on rank one idempotents (English)
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16 August 2004
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In [J. Funct. Anal. 194, 248--262 (2002; Zbl 1010.46023)], \textit{L. Molnár} characterized bijective transformations preserving zero products in both directions on the set of all rank one idempotent operators on a Banach space. In the paper under review, the present author gives a short proof of Molnár's results as well as an improvement in the finite-dimensional case. These results are applied to describe automorphisms of standard operator semigroups and to improve Uhlhorn's version of Wigner's theorem.
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idempotent operators
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indefinite inner product space
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orthogonality preserving transformations
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