Geodesic
Products of Involutions of an Infinite-dimensional Vector Space
Canadian journal of mathematics, Tome 73 (2021) no. 1, pp. 195-220

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DOI

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 $2$.
DOI : 10.4153/S0008414X19000579
Mots-clés : infinite dimension, decomposition, involution, quadratic automorphism, ordinal, bilateral shift 
Pazzis, Clément de Seguins. Products of Involutions of an Infinite-dimensional Vector Space. Canadian journal of mathematics, Tome 73 (2021) no. 1, pp. 195-220. doi: 10.4153/S0008414X19000579
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     title = {Products of {Involutions} of an {Infinite-dimensional} {Vector} {Space}},
     journal = {Canadian journal of mathematics},
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     year = {2021},
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     doi = {10.4153/S0008414X19000579},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000579/}
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