### Abstract

In this paper, we prove the following: (1) If T is invertible ω-hyponormal completely non-normal, then the point spectrum is empty. (2) If T_{1} and T_{2} are injective ω-hyponormal and if T and S are quasisimilar, then they have the same spectra and essential spectra. (3) If T is (p, k)-quasihyponormal operator, then σ_{jp}(T)-{0} = σap(T)-{0}. (4) If T^{*}, S ∈ B(H) are injective (p, k)-quasihyponormal operator, and if XT =SX, where X ∈B(H) is an invertible, then there exists a unitary operator U such that UT = SU and hence T and S are normal operators.

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

Pages (from-to) | 135-143 |

Number of pages | 9 |

Journal | Bulletin of the Malaysian Mathematical Sciences Society |

Volume | 31 |

Issue number | 2 |

Publication status | Published - 2008 |

### Fingerprint

### Keywords

- ω-hyponormal
- (p,k)-quasihyponormal
- Class A
- Quasisimilarity
- Weyl's theorem

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the Malaysian Mathematical Sciences Society*,

*31*(2), 135-143.

**On the spectra of some non-normal operators.** / Rashid, M. H M; Md. Noorani, Mohd. Salmi; Saari, A. S.

Research output: Contribution to journal › Article

*Bulletin of the Malaysian Mathematical Sciences Society*, vol. 31, no. 2, pp. 135-143.

}

TY - JOUR

T1 - On the spectra of some non-normal operators

AU - Rashid, M. H M

AU - Md. Noorani, Mohd. Salmi

AU - Saari, A. S.

PY - 2008

Y1 - 2008

N2 - In this paper, we prove the following: (1) If T is invertible ω-hyponormal completely non-normal, then the point spectrum is empty. (2) If T1 and T2 are injective ω-hyponormal and if T and S are quasisimilar, then they have the same spectra and essential spectra. (3) If T is (p, k)-quasihyponormal operator, then σjp(T)-{0} = σap(T)-{0}. (4) If T*, S ∈ B(H) are injective (p, k)-quasihyponormal operator, and if XT =SX, where X ∈B(H) is an invertible, then there exists a unitary operator U such that UT = SU and hence T and S are normal operators.

AB - In this paper, we prove the following: (1) If T is invertible ω-hyponormal completely non-normal, then the point spectrum is empty. (2) If T1 and T2 are injective ω-hyponormal and if T and S are quasisimilar, then they have the same spectra and essential spectra. (3) If T is (p, k)-quasihyponormal operator, then σjp(T)-{0} = σap(T)-{0}. (4) If T*, S ∈ B(H) are injective (p, k)-quasihyponormal operator, and if XT =SX, where X ∈B(H) is an invertible, then there exists a unitary operator U such that UT = SU and hence T and S are normal operators.

KW - ω-hyponormal

KW - (p,k)-quasihyponormal

KW - Class A

KW - Quasisimilarity

KW - Weyl's theorem

UR - http://www.scopus.com/inward/record.url?scp=70349251720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349251720&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:70349251720

VL - 31

SP - 135

EP - 143

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

SN - 0126-6705

IS - 2

ER -