Weyl's Type Theorems for Quasi-Class A Operators
M.H.M. Rashid, M.S.M. Noorani and A.S. Saari
DOI : 10.3844/jmssp.2008.70.74
Journal of Mathematics and Statistics
Volume 4, Issue 2
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.
© 2008 M.H.M. Rashid, M.S.M. Noorani and A.S. Saari. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.