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arXiv · 1808.02224

Products of involutions of an infinite-dimensional vector space

Clément de Seguins Pazzis
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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 $2$.

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Clément de Seguins Pazzis. 2018-08-07. Products of involutions of an infinite-dimensional vector space. https://arxiv.org/abs/1808.02224

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