1999/09/17 by Sergej A. Choroszavin, Choroszavin, Sergej A.
Engineering · Materials Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Metal Forming Simulation Techniques #Microstructure and mechanical properties #Numerical methods in engineering #Representation Theory (math.RT) #Spectral Theory (math.SP) #math-ph #math.FA #math.MP #math.RT #math.SP
paper · pdf · doi:10.48550/arxiv.math/9909101
Latex 2.09
openalex publication_date 1999/09/17 · arxiv created 2003/12/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Definition. Let J be a period-2 unitary operator (some people say J is reflection operator or reflection symmetry) and U be a linear operator. If U^*JU = J (resp. U^*JU >= J) then U is said to be J-isometry (resp. J-noncontraction). If U^*JU >= J and UJU^* >= J) then U is said to be J-binoncontraction). Theorem. If every J-isometry has nontrivial positive invariant subspace then every J-noncontraction has such a subspace. Theorem. If every J-binoncontractive J-isometry has maximal positive invariant subspace then every J-noncontraction has such a subspace. The article text is the complete text of the author's report on 15-th Voronezh Winter Mathematical School, p 119 (see. VINITI 16.12.81, N 5691-81). But in that time the presented construtions and theorems seemed to be rather curious observations. Now the situattion is changing (see e.g. math.DS/9908169)