Research Article Open Access

Weyl's Type Theorems for Quasi-Class A Operators

M.H.M. Rashid, M.S.M. Noorani and A.S. Saari

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.

Journal of Mathematics and Statistics
Volume 4 No. 2, 2008, 70-74

DOI: https://doi.org/10.3844/jmssp.2008.70.74

Submitted On: 6 September 2007 Published On: 30 June 2008

How to Cite: Rashid, M., Noorani, M. & Saari, A. (2008). Weyl's Type Theorems for Quasi-Class A Operators. Journal of Mathematics and Statistics, 4(2), 70-74. https://doi.org/10.3844/jmssp.2008.70.74

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Keywords

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