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Products of roots of the identity

Author(s): M. Hladnik; M. Omladic; H. Radjavi
Journal: Proc. Amer. Math. Soc. 129 (2001), 459-465.
MSC (2000): Primary 47A65; Secondary 47B47, 47D03
Posted: August 28, 2000
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Abstract:

It is proved that every invertible bounded linear operator on a complex infinite-dimensional Hilbert space is a product of five $n$-th roots of the identity for every $n > 2$. For invertible normal operators four factors suffice in general.

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L. Grunenfelder, T. Kosir, M. Omladic, and H. Radjavi, On groups generated by elements of prime order, Geom. Dedicata 75 (1999), 317-332. CMP 99:14

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Additional Information:

M. Hladnik
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
Email: milan.hladnik@fmf.uni-lj.si

M. Omladic
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
Email: matjaz.omladic@fmf.uni-lj.si

H. Radjavi
Affiliation: Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Email: radjavi@mscs.dal.ca

DOI: 10.1090/S0002-9939-00-05563-5
PII: S 0002-9939(00)05563-5
Keywords: Invertible operators, normal operators, compact operators, roots of the identity, group commutators
Received by editor(s): September 1, 1998
Received by editor(s) in revised form: April 20, 1999
Posted: August 28, 2000
Additional Notes: This work was supported in part by the Ministry of Science and Technology of Slovenia and by the NSERC of Canada.
Communicated by: David R. Larson
Copyright of article: Copyright 2000, American Mathematical Society

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