Sums of quadratic endomorphisms of an infinite-dimensional vector space
Rings and Algebras
2016-09-27 v2
Abstract
We prove that every endomorphism of an infinite-dimensional vector space splits as the sum of four idempotents and as the sum of four square-zero endomorphisms, a result that is optimal in general.
Keywords
Cite
@article{arxiv.1601.00296,
title = {Sums of quadratic endomorphisms of an infinite-dimensional vector space},
author = {Clément de Seguins Pazzis},
journal= {arXiv preprint arXiv:1601.00296},
year = {2016}
}
Comments
14 pages (Proposition 5 contained an error in earlier versions: it has been corrected)