The group generated by unipotent operators
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- by C. K. Fong and A. R. Sourour PDF
- Proc. Amer. Math. Soc. 97 (1986), 453-458 Request permission
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.References
- Arlen Brown and Carl Pearcy, Structure of commutators of operators, Ann. of Math. (2) 82 (1965), 112–127. MR 178354, DOI 10.2307/1970564
- Kenneth Hoffman and Ray Kunze, Linear algebra, 2nd ed., Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0276251
- Irving Kaplansky, Fields and rings, 2nd ed., Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1972. MR 0349646
- H. Radjavi, The group generated by involutions, Proc. Roy. Irish Acad. Sect. A 81 (1981), no. 1, 9–12. MR 635572
- Heydar Radjavi and Peter Rosenthal, Invariant subspaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 77, Springer-Verlag, New York-Heidelberg, 1973. MR 0367682
- Gian-Carlo Rota, On models for linear operators, Comm. Pure Appl. Math. 13 (1960), 469–472. MR 112040, DOI 10.1002/cpa.3160130309
Additional Information
- © Copyright 1986 American Mathematical Society
- 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