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On hypo-Jordan operators

Published online by Cambridge University Press:  25 July 2002

Eungil Ko
Eungil Ko
Affiliation:
Department of Mathematics, Ewha Women's University, Seoul 120-750, Korea e-mail: [email protected]
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In this paper, we show that if T=S+N, where S is similar to a hyponormal operator, S and N commute and N is a nilpotent operator of order m (i.e., N^m=0), then T is a subscalar operator of order 2m. As a corollary, we get that such a T has a nontrivial invariant subspace if its spectrum \sigma(T\hskip1) has the property that there exists some non-empty open set U such that \sigma(T\hskip1)\capU is dominating for U.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 3 , May 2001 , pp. 411 - 418
Copyright
2001 Glasgow Mathematical Journal Trust