Products of roots of the identity
HTML articles powered by AMS MathViewer
- by M. Hladnik, M. Omladič and H. Radjavi PDF
- Proc. Amer. Math. Soc. 129 (2001), 459-465 Request permission
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.References
- Arlen Brown and Carl Pearcy, Multiplicative commutators of operators, Canadian J. Math. 18 (1966), 737–749. MR 200720, DOI 10.4153/CJM-1966-074-1
- D. Ž. Djoković, Product of two involutions, Arch. Math. (Basel) 18 (1967), 582–584. MR 219550, DOI 10.1007/BF01898863
- L. Grunenfelder, T. Košir, M. Omladič, and H. Radjavi, On groups generated by elements of prime order, Geom. Dedicata 75 (1999), 317–332.
- W. H. Gustafson, P. R. Halmos, and H. Radjavi, Products of involutions, Linear Algebra Appl. 13 (1976), no. 1-2, 157–162. Collection of articles dedicated to Olga Taussky Todd. MR 399284, DOI 10.1016/0024-3795(76)90054-9
- S. S. Pillai, On normal numbers, Proc. Indian Acad. Sci., Sect. A. 10 (1939), 13–15. MR 0000020, DOI 10.1007/BF03170534
- H. Radjavi, The group generated by involutions, Proc. Roy. Irish Acad. Sect. A 81 (1981), no. 1, 9–12. MR 635572
- María J. Wonenburger, Transformations which are products of two involutions, J. Math. Mech. 16 (1966), 327–338. MR 0206025, DOI 10.1512/iumj.1967.16.16023
Additional Information
- M. Hladnik
- Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
- Email: milan.hladnik@fmf.uni-lj.si
- M. Omladič
- 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
- MR Author ID: 143615
- Email: radjavi@mscs.dal.ca
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 459-465
- MSC (2000): Primary 47A65; Secondary 47B47, 47D03
- DOI: https://doi.org/10.1090/S0002-9939-00-05563-5
- MathSciNet review: 1707518