Cyclic decomposition of unitary spaces
type: Item
instance of: scholarly article
title: Cyclic decomposition of unitary spaces
zbMATH Open document ID: 0539.51008
DOI: 10.1007/BF01918134
published in: Journal of Geometry
publication date: 1983-01-01T00:00:00Z
review text: The main result of the present paper is: If \(\pi\) is a unitary transformation that is similar to its inverse, then the vector space V is an orthogonal sum of regular \(\pi\)-cyclic and \(\pi\)-bicyclic subspaces. For arbitrary unitary spaces this does not imply that \(\pi\) is a product of two unitary involutions, although \(\pi\) is a product of involutions in GL(V). But a unitary transformation \(\pi\) of a complex inner product space is a product of two unitary involutions if the spectrum of \(\pi\) is symmetric to the real axis.
Mathematics Subject Classification ID: 51F25
Mathematics Subject Classification ID: 20H20
zbMATH DE Number: 3857841
zbMATH Keywords: unitary transformation
zbMATH Keywords: orthogonal decomposition
zbMATH Keywords: unitary involutions
author: Erich W. Ellers
MaRDI profile type: Publication
cites work: Q3265046
cites work: Bireflectionality in Classical Groups
cites work: Bireflectionality of orthogonal and symplectic groups
cites work: Products of two involutions in classical groups of characteristic 2
cites work: Isometrien von Vektorräumen. I
cites work: Q5553361
full work available at URL: https://doi.org/10.1007/bf01918134
OpenAlex ID: W2010873622
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description: scientific article; zbMATH DE number 3857841