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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The group generated by unipotent operators


Authors: C. K. Fong and A. R. Sourour
Journal: Proc. Amer. Math. Soc. 97 (1986), 453-458
MSC: Primary 47D10; Secondary 15A30, 47A05
DOI: https://doi.org/10.1090/S0002-9939-1986-0840628-0
MathSciNet review: 840628
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Abstract: The group generated by unipotent $ n \times n$ complex matrices is $ {\text{S}}{{\text{L}}_n}(C)$, and every member of the latter is a product of three unipotent matrices. The group generated by unipotent operators on Hilbert space $ \mathcal{H}$ is $ {\text{GL(}}\mathcal{H}{\text{)}}$, and every invertible operator is a product of six unipotent operators of order 2.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0840628-0
Article copyright: © Copyright 1986 American Mathematical Society