Some results on extremal vectors and invariant subspaces
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- by Per Enflo and Terje Hõim PDF
- Proc. Amer. Math. Soc. 131 (2003), 379-387 Request permission
Abstract:
In 1996 P. Enflo introduced the concept of extremal vectors and their connection to the Invariant Subspace Problem. The study of backward minimal vectors gives a new method of finding invariant subspaces which is more constructive than the previously known methods. In this article we study the properties and behaviour of extremal vectors, give some new formulas related to backward minimal vectors and improve results from papers by Ansari and Enflo (1998) and Enflo (1998).References
- Shamim Ansari and Per Enflo, Extremal vectors and invariant subspaces, Trans. Amer. Math. Soc. 350 (1998), no. 2, 539–558. MR 1407476, DOI 10.1090/S0002-9947-98-01865-0
- Per Enflo, Extremal vectors for a class of linear operators, Functional analysis and economic theory (Samos, 1996) Springer, Berlin, 1998, pp. 61–64. MR 1730119, DOI 10.1007/978-3-642-72222-6_{5}
- P. Enflo, V. Lomonosov, Some aspects of the Invariant Subspace Problem, to appear.
Additional Information
- Per Enflo
- Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44242
- Email: enflo@mcs.kent.edu
- Terje Hõim
- Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44242
- MR Author ID: 653599
- Email: terje.hoim@trincoll.edu
- Received by editor(s): August 15, 2000
- Received by editor(s) in revised form: February 7, 2001
- Published electronically: September 17, 2002
- Additional Notes: The first author was supported by an NSF grant
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 379-387
- MSC (2000): Primary 47A15
- DOI: https://doi.org/10.1090/S0002-9939-02-06326-8
- MathSciNet review: 1933328