### Abstract

A variant of Weyl theorem for a class of quasi-class A acting on an infinite complex Hilbert space were discussed. If the adjoint of T is a quasi-class A operator, then the generalized a-Weyl holds for f(T) , for every function that analytic on the spectrum of T. The generalized Weyl theorem holds for a quasi-class A was proved. Also, a characterization of the Hilbert space as a direct sum of range and kernel of a quasi-class A was given. Among other things, if the operator is a quasi-class A, then the B-Weyl spectrum satisfies the spectral theorem was characterized.

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

Pages (from-to) | 70-74 |

Number of pages | 5 |

Journal | Journal of Mathematics and Statistics |

Volume | 4 |

Issue number | 2 |

Publication status | Published - 2008 |

### Fingerprint

### Keywords

- Browder's spectrum theory
- Fredholm theory
- Single valued extension property

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Journal of Mathematics and Statistics*,

*4*(2), 70-74.

**Weyl's type theorems for quasi-class a operators.** / Rashid, M. H M; Md. Noorani, Mohd. Salmi; Saari, A. S.

Research output: Contribution to journal › Article

*Journal of Mathematics and Statistics*, vol. 4, no. 2, pp. 70-74.

}

TY - JOUR

T1 - Weyl's type theorems for quasi-class a operators

AU - Rashid, M. H M

AU - Md. Noorani, Mohd. Salmi

AU - Saari, A. S.

PY - 2008

Y1 - 2008

N2 - A variant of Weyl theorem for a class of quasi-class A acting on an infinite complex Hilbert space were discussed. If the adjoint of T is a quasi-class A operator, then the generalized a-Weyl holds for f(T) , for every function that analytic on the spectrum of T. The generalized Weyl theorem holds for a quasi-class A was proved. Also, a characterization of the Hilbert space as a direct sum of range and kernel of a quasi-class A was given. Among other things, if the operator is a quasi-class A, then the B-Weyl spectrum satisfies the spectral theorem was characterized.

AB - A variant of Weyl theorem for a class of quasi-class A acting on an infinite complex Hilbert space were discussed. If the adjoint of T is a quasi-class A operator, then the generalized a-Weyl holds for f(T) , for every function that analytic on the spectrum of T. The generalized Weyl theorem holds for a quasi-class A was proved. Also, a characterization of the Hilbert space as a direct sum of range and kernel of a quasi-class A was given. Among other things, if the operator is a quasi-class A, then the B-Weyl spectrum satisfies the spectral theorem was characterized.

KW - Browder's spectrum theory

KW - Fredholm theory

KW - Single valued extension property

UR - http://www.scopus.com/inward/record.url?scp=57049127086&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57049127086&partnerID=8YFLogxK

M3 - Article

VL - 4

SP - 70

EP - 74

JO - Journal of Mathematics and Statistics

JF - Journal of Mathematics and Statistics

SN - 1549-3644

IS - 2

ER -