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Products of Involutions of an Infinite-dimensional Vector Space
Published online by Cambridge University Press: 15 November 2019
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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- © Canadian Mathematical Society 2019
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