Applying projective geometry to transformations on rank one idempotents
type: Item
instance of: scholarly article
title: Applying projective geometry to transformations on rank one idempotents
zbMATH Open document ID: 1062.47039
author: Peter Šemrl
published in: Journal of Functional Analysis
publication date: 2004-08-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 47B49
Mathematics Subject Classification ID: 47B48
Mathematics Subject Classification ID: 46C20
Mathematics Subject Classification ID: 47B50
zbMATH DE Number: 2091746
zbMATH Keywords: idempotent operators
zbMATH Keywords: indefinite inner product space
zbMATH Keywords: orthogonality preserving transformations
reviewed by: Jianlian Cui
MaRDI profile type: Publication
full work available at URL: j.jfa.2003.07.009
OpenAlex ID: W2035710903
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DOI: 10.1016/J.JFA.2003.07.009
description: scientific article; zbMATH DE number 2091746