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 $2$.

中文翻译：

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无限维向量空间的对合乘积

我们证明了一个域上无限维向量空间的每一个自同构都是四次对合的乘积，这个结果在一般情况下是最优的。我们还刻画了三个对合乘积的自同构。更一般地说，我们研究将自同构分解成三个或四个因子，并使用规定的 $2$ 次分裂湮灭多项式。