Applying projective geometry to transformations on rank one idempotents
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.
orthogonality preserving transformations
scientific article; zbMATH DE number 2091746
scientific article