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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Products of roots of the identity


Authors: M. Hladnik, M. Omladic and H. Radjavi
Journal: Proc. Amer. Math. Soc. 129 (2001), 459-465
MSC (2000): Primary 47A65; Secondary 47B47, 47D03
Published electronically: August 28, 2000
MathSciNet review: 1707518
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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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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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2000 American Mathematical Society