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On rank-one perturbations of normal operators

Authors:	C Foias IB Jung E Ko C Pearcy

Institution:	^aDepartment of Mathematics, Texas A&M University, College Station, TX 77843, USA;^bDepartment of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-701, Republic of Korea;^cDepartment of Mathematics, Ewha Women's University, Seoul 120-750, Republic of Korea

Abstract:	This paper is concerned with operators on Hilbert space of the form T=D+uv where D is a diagonalizable normal operator and uv is a rank-one operator. It is shown that if and the vectors u and v have Fourier coefficients and with respect to an orthonormal basis that diagonalizes D that satisfy , then T has a nontrivial hyperinvariant subspace. This partially answers an open question of at least 30 years duration.

Keywords:	Invariant subspace Hyperinvariant subspace Normal operator Rank-one perturbation
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