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Sums of Quadratic Endomorphisms of an Infinite-Dimensional Vector Space

Part of: General and miscellaneous Basic linear algebra

Published online by Cambridge University Press:  26 February 2018

Clément de Seguins Pazzis
Clément de Seguins Pazzis*
Affiliation:
Université de Versailles Saint-Quentin-en-Yvelines, Laboratoire de Mathématiques de Versailles, 45 avenue des États-Unis, 78035 Versailles cedex, France ([email protected])
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Abstract

We prove that every endomorphism of an infinite-dimensional vector space over a field splits into the sum of four idempotents and into the sum of four square-zero endomorphisms, a result that is optimal in general.

Keywords

infinite dimensiondecompositionsquare-zero endomorphismidempotentordinals

MSC classification

Primary: 15A24: Matrix equations and identities 16B50: Category-theoretic methods and results (except as in )
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 2 , May 2018 , pp. 437 - 447
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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