### Abstract

For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If T* is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)), where Hol(σ(T)) is the space of all functions that analytic in an open neighborhoods of σ(T) of T. (c) If T* is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)). (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum σ _{SBF} ^{-} _{+}(T), and for left Drazin spectrum σ _{lD}(T) for every f ∈ Hol(σ(T)).

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

Pages (from-to) | 77-95 |

Number of pages | 19 |

Journal | Communications of the Korean Mathematical Society |

Volume | 27 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 |

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### Keywords

- (p, k)-quasihyponormal
- Browder's theory
- Fredholm theory
- Single valued extension property
- Spectrum

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Weyl's type theorems for algebraically (p, k)-quasihyponormal operators.** / Rashid, Mohammad Hussein Mohammad; Md. Noorani, Mohd. Salmi.

Research output: Contribution to journal › Article

*Communications of the Korean Mathematical Society*, vol. 27, no. 1, pp. 77-95. https://doi.org/10.4134/CKMS.2012.27.1.077

}

TY - JOUR

T1 - Weyl's type theorems for algebraically (p, k)-quasihyponormal operators

AU - Rashid, Mohammad Hussein Mohammad

AU - Md. Noorani, Mohd. Salmi

PY - 2012

Y1 - 2012

N2 - For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If T* is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)), where Hol(σ(T)) is the space of all functions that analytic in an open neighborhoods of σ(T) of T. (c) If T* is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)). (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum σ SBF - +(T), and for left Drazin spectrum σ lD(T) for every f ∈ Hol(σ(T)).

AB - For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If T* is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)), where Hol(σ(T)) is the space of all functions that analytic in an open neighborhoods of σ(T) of T. (c) If T* is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)). (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum σ SBF - +(T), and for left Drazin spectrum σ lD(T) for every f ∈ Hol(σ(T)).

KW - (p, k)-quasihyponormal

KW - Browder's theory

KW - Fredholm theory

KW - Single valued extension property

KW - Spectrum

UR - http://www.scopus.com/inward/record.url?scp=84857854855&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857854855&partnerID=8YFLogxK

U2 - 10.4134/CKMS.2012.27.1.077

DO - 10.4134/CKMS.2012.27.1.077

M3 - Article

AN - SCOPUS:84857854855

VL - 27

SP - 77

EP - 95

JO - Communications of the Korean Mathematical Society

JF - Communications of the Korean Mathematical Society

SN - 1225-1763

IS - 1

ER -