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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… Click to show full 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 $2$.
Keywords:
dimensional vector;
infinite dimensional;
products involutions;
vector space
Journal Title: Canadian Journal of Mathematics
Year Published: 2019
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Journal Title: Canadian Journal of Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!