Weyl's type theorems for quasi-class a operators

M. H M Rashid, Mohd. Salmi Md. Noorani, A. S. Saari

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)70-74
Number of pages5
JournalJournal of Mathematics and Statistics
Volume4
Issue number2
Publication statusPublished - 2008

Fingerprint

Operator
Theorem
Weyl's Theorem
Hilbert space
Spectral Theorem
Direct Sum
Thing
Class
Analytic function
kernel
Range of data

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

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

In: Journal of Mathematics and Statistics, Vol. 4, No. 2, 2008, p. 70-74.

Research output: Contribution to journalArticle

@article{cf6d45ab2b034650b34a5e7017b6c6eb,
title = "Weyl's type theorems for quasi-class a operators",
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.",
keywords = "Browder's spectrum theory, Fredholm theory, Single valued extension property",
author = "Rashid, {M. H M} and {Md. Noorani}, {Mohd. Salmi} and Saari, {A. S.}",
year = "2008",
language = "English",
volume = "4",
pages = "70--74",
journal = "Journal of Mathematics and Statistics",
issn = "1549-3644",
publisher = "Science Publications",
number = "2",

}

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

AN - SCOPUS:57049127086

VL - 4

SP - 70

EP - 74

JO - Journal of Mathematics and Statistics

JF - Journal of Mathematics and Statistics

SN - 1549-3644

IS - 2

ER -