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Some results on extremal vectors and invariant subspaces
Authors:
Per Enflo and Terje Hõim
Journal:
Proc. Amer. Math. Soc. 131 (2003), 379-387
MSC (2000):
Primary 47A15
Posted:
September 17, 2002
MathSciNet review:
1933328
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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).
- 1.
Shamim
Ansari and Per
Enflo, Extremal vectors and invariant
subspaces, Trans. Amer. Math. Soc.
350 (1998), no. 2,
539–558. MR 1407476
(98d:47019), http://dx.doi.org/10.1090/S0002-9947-98-01865-0
- 2.
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
(2000k:47020)
- 3.
P. Enflo, V. Lomonosov, Some aspects of the Invariant Subspace Problem, to appear.
- 1.
- S. Ansari, P. Enflo, Extremal vectors and invariant subspaces, Trans. Amer. Math. Soc. 350 (1998), 539-558. MR 98d:47019
- 2.
- P. Enflo, Extremal vectors for a class of linear operators, Functional Analysis and Economic Theory, Springer-Verlag (1998), 61-64. MR 2000k:47020
- 3.
- P. Enflo, V. Lomonosov, Some aspects of the Invariant Subspace Problem, to appear.
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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
Email:
terje.hoim@trincoll.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-02-06326-8
PII:
S 0002-9939(02)06326-8
Keywords:
Invariant subspaces,
extremal vectors
Received by editor(s):
August 15, 2000
Received by editor(s) in revised form:
February 7, 2001
Posted:
September 17, 2002
Additional Notes:
The first author was supported by an NSF grant
Communicated by:
N. Tomczak-Jaegermann
Article copyright:
© Copyright 2002 American Mathematical Society
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