Journal of Operator Theory

Volume 54, Issue 2, Fall 2005 pp. 401-414.

On quasinilpotent operators. III

Authors: C. Foias (1), I.B. Jung (2), E. Ko (3), and C. Pearcy (4)
Author institution: (1) Department of Mathematics, Texas A\&M University, College Station, TX 77843, USA, (2) Department of Mathematics, College of Natural Science, Kyungpook National University, Taegu 702-701, Korea, (3) Department of Mathematics, Ewha Women's University, Seoul 120--750, Korea, (4) Department of Mathematics, Texas A\&M University, College Station, TX 77843, USA

Summary: This paper is a continuation of our study [9], [3] of quasinilpotent operators in which we obtain some new hyperinvariant-subspace theorems for such operators. We also prove a structure theorem about certain quasinilpotent operators and reduce the hyperinvariant subspace problem for quasinilpotent operators to a special subcase.

Keywords: Quasinilpotent operators, invariant subspaces, hyperinvariant subspaces

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