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Products of Involutions of an Infinite-dimensional Vector Space

Part of: Basic linear algebra

Published online by Cambridge University Press:  15 November 2019

Clément de Seguins Pazzis
Clément de Seguins Pazzis*
Affiliation:
Université de Versailles Saint-Quentin-en-Yvelines, Laboratoire de Mathématiques de Versailles, 45 avenue des Etats-Unis, 78035Versailles cedex, France Email: dsp.prof@gmail.com
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Abstract

We prove that every automorphism of an infinite-dimensional vector space over a field is the product of four involutions, a result that is optimal in the general case. We also characterize the automorphisms that are the product of three involutions. More generally, we study decompositions of automorphisms into three or four factors with prescribed split annihilating polynomials of degree $2$.

Keywords

infinite dimensiondecompositioninvolutionquadratic automorphismordinalbilateral shift

MSC classification

Primary: 15A23: Factorization of matrices
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 1 , February 2021 , pp. 195 - 220
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Copyright
© Canadian Mathematical Society 2019

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