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On quasinilpotent Operators, II

Published online by Cambridge University Press:  09 April 2009

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.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Ansari, S. and Enflo, P., ‘Extremal vectors and invariant subspaces’, Trans. Amer. Math. Soc. 350 (1998), 539558.CrossRefGoogle 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), 399404.Google Scholar
[4]Jung, I., Ko, E. and Pearcy, C., ‘On quasinilpotent operators’, Proc. Amer. Math. Soc. 131 (2003), 21212127.CrossRefGoogle Scholar
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[6]Lomonosov, V., ‘An extension of Burnside's theorem to infinite dimensional spaces’, Israel J. Math. 75 (1991), 329339.CrossRefGoogle Scholar
[7]Pearcy, C. and Salinas, N., ‘An invariant subspace theorem’, Michigan Math. J. 20 (1973), 2131.Google 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. 219230.CrossRefGoogle Scholar
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