Variations of Weyl Type Theorems

A Banach space operator T satisfies property(Bgw), a variant property(gw), if the complement in the approximate point spectrum σa(T ) of the semi-B-essential approximate point spectrum σSBF− + (T ) coincides with set of isolated eigenvalues of T of finite multiplicity E(T ). We also introduce properties (Bb), and property (Bgb) in connection with Weyl type theorems, which are analogous, respectively, to generalized Browder’s theorem and property(gb). We obtain relation among these new properties. 1 Department of Mathematics, Faculty of Science P.O. Box(7), Mu’tah university, Al-Karak, Jordan. E-mail address: malik [email protected] 2 Department of Science and Humanities, Ahalia School of Engineering and Technology, Palakkad -678557, Kerala, India. E-mail address: [email protected] Date: Received: 1 May 2012; Revised: 12 August 2012; Accepted: 8 September 2012. ∗ Corresponding author. 2010 Mathematics Subject Classification. Primary 47A10; Secondary 47A11, 47A53.