### Abstract

Let T be a bounded linear operator acting on a Hilbert space H. It is shown that, if T or its adjoint T* is w-hyponormal, then the generalized Weyl theorem holds for f for every f ε Hole(σ(T) We also show that if T* is w-hyponormal, then the generalized a-Weyl theorem holds for f(T) for every f ε Hole(σ(T) and the B-Weyl spectrum σBW(T) and the semi-B-Fredholm spectrum σSBF_{+-}(T) of T satisfies the spectral mapping theorem. Finally, we examine the stability of the generalized a-Weyl's theorem under commutative perturbations by finite rank operators.

Original language | English |
---|---|

Pages (from-to) | 103-116 |

Number of pages | 14 |

Journal | Arabian Journal for Science and Engineering |

Volume | 35 |

Issue number | 1 D |

Publication status | Published - May 2010 |

### Fingerprint

### Keywords

- B-Fredholm theory
- Browder's theory
- Semi-B-Fredholm
- Single valued extension property
- Spectrum
- w-hyponormal operators

### ASJC Scopus subject areas

- General

### Cite this

*Arabian Journal for Science and Engineering*,

*35*(1 D), 103-116.

**Weyl's type theorems for algebraically w-hyponormal operators.** / Rashid, M. H M; Md. Noorani, Mohd. Salmi.

Research output: Contribution to journal › Article

*Arabian Journal for Science and Engineering*, vol. 35, no. 1 D, pp. 103-116.

}

TY - JOUR

T1 - Weyl's type theorems for algebraically w-hyponormal operators

AU - Rashid, M. H M

AU - Md. Noorani, Mohd. Salmi

PY - 2010/5

Y1 - 2010/5

N2 - Let T be a bounded linear operator acting on a Hilbert space H. It is shown that, if T or its adjoint T* is w-hyponormal, then the generalized Weyl theorem holds for f for every f ε Hole(σ(T) We also show that if T* is w-hyponormal, then the generalized a-Weyl theorem holds for f(T) for every f ε Hole(σ(T) and the B-Weyl spectrum σBW(T) and the semi-B-Fredholm spectrum σSBF+-(T) of T satisfies the spectral mapping theorem. Finally, we examine the stability of the generalized a-Weyl's theorem under commutative perturbations by finite rank operators.

AB - Let T be a bounded linear operator acting on a Hilbert space H. It is shown that, if T or its adjoint T* is w-hyponormal, then the generalized Weyl theorem holds for f for every f ε Hole(σ(T) We also show that if T* is w-hyponormal, then the generalized a-Weyl theorem holds for f(T) for every f ε Hole(σ(T) and the B-Weyl spectrum σBW(T) and the semi-B-Fredholm spectrum σSBF+-(T) of T satisfies the spectral mapping theorem. Finally, we examine the stability of the generalized a-Weyl's theorem under commutative perturbations by finite rank operators.

KW - B-Fredholm theory

KW - Browder's theory

KW - Semi-B-Fredholm

KW - Single valued extension property

KW - Spectrum

KW - w-hyponormal operators

UR - http://www.scopus.com/inward/record.url?scp=79951874146&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951874146&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79951874146

VL - 35

SP - 103

EP - 116

JO - Arabian Journal for Science and Engineering

JF - Arabian Journal for Science and Engineering

SN - 1319-8025

IS - 1 D

ER -