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On quasinilpotent Operators, II

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Ciprian Foiaş ,
Il Bong Jung ,
Eungil Ko  and
Carl Pearcy
Ciprian Foiaş
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA e-mail: foias@math.tamu.edu
Il Bong Jung
Affiliation:
Department of Mathematics, College of Natural Science, Kyungpook National University, Daegu 702–701, Korea e-mail: ibjung@knu.ac.kr
Eungil Ko
Affiliation:
Department of Mathematics, Ewha Women's University, Seoul 120–750, Korea e-mail: eiko@ewha.ac.kr
Carl Pearcy
Affiliation:
Department of Mathematics, Texas A&M University, College Station TX 77843, USA e-mail: pearcy@math.tamu.edu
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Abstract

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In this paper we continue to modify and expand a technique due to Enflo for producing nontrivial hyperinvariant subspaces for quasinilpotent operators, and thereby obtain such subspaces for some additional quasinilpotent operators on Hilbert space. We also obtain a structure theorem for a certain class of operators.

Keywords

hyperinvariant subspacesquasinilpotent operators

MSC classification

Secondary: 47A15: Invariant subspaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 3 , December 2004 , pp. 349 - 356
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Ansari, S. and Enflo, P., ‘Extremal vectors and invariant subspaces’, Trans. Amer. Math. Soc. 350 (1998), 539–558.Google Scholar
[2]Bercovici, H., Foiaş, C. and Pearcy, C., Dual algebras with applications to invariant subspaces and dilation theory, CBMS Regional Conference Series in Mathematics 56 (Amer. Math. Soc., Providence, RI, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1985).CrossRefGoogle Scholar
[3]Foiaş, C. and Pearcy, C., ‘A model for quasinilpotent operators’, Michigan Math. J. 21 (1974), 399–404.Google Scholar
[4]Jung, I., Ko, E. and Pearcy, C., ‘On quasinilpotent operators’, Proc. Amer. Math. Soc. 131 (2003), 2121–2127.CrossRefGoogle Scholar
[5]Lomonosov, V., ‘On invariant subspaces of families of operators commuting with a completely continuous operator’, Funktsional. Anal. i Prilozen. 7 (1973), 55–56.Google Scholar
[6]Lomonosov, V., ‘An extension of Burnside's theorem to infinite dimensional spaces’, Israel J. Math. 75 (1991), 329–339.Google Scholar
[7]Pearcy, C. and Salinas, N., ‘An invariant subspace theorem’, Michigan Math. J. 20 (1973), 21–31.CrossRefGoogle Scholar
[8]Pearcy, C. and Shields, A., ‘A survey of the Lomonosov technique in the theory of invariant subspaces’, in: Topics in operator theory, Math. Surveys 13 (Amer. Math. Soc., Providence, RI, 1974) pp. 219–230.Google Scholar