## Abstract

The Aluthge transform T̃ (defined below) of an operator T on Hilbert space has been studied extensively, most often in connection with p-hyponormal operators. In [6] the present authors initiated a study of various relations between an arbitrary operator T and its associated T̃, and this study was continued in [7], in which relations between the spectral pictures of T and T̃ were obtained. This article is a continuation of [6] and [7]. Here we pursue the study of the sequence of Aluthge iterates {T̃^{(n)}} associated with an arbitrary operator T. In particular, we verify that in certain cases the sequence {T̃^{(n)}}converges to a normal operator, which partially answers Conjecture 1.11 in [6] and its modified version below (Conjecture 5.6).

Original language | English |
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Pages (from-to) | 375-387 |

Number of pages | 13 |

Journal | Integral Equations and Operator Theory |

Volume | 45 |

Issue number | 4 |

DOIs | |

State | Published - 2003 |

### Bibliographical note

Funding Information:The first author was partially supported by KOSEF Research Project No. R01-2000-00003. The second author was supported by Korea Research Foundation Grant (KRF-2000-015-DP0023). The third author appreciates the support of the National Science Foundation.

## Keywords

- Aluthge transform
- p-hyponormal operator
- Quasinilpotent operator
- Wighted shift