Products of involutions of an infinite-dimensional vector space

2018/08/07 by Clément de Seguins Pazzis, Pazzis, Clément de Seguins
Mathematics · #15A24 #16B50 #Advanced Banach Space Theory #FOS: Mathematics #Rings and Algebras (math.RA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1808.02224

openalex publication_date 2018/08/07 · openalex created_date 2018/08/22 · openalex updated_date 2026/07/28

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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