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in this paper we establish the relation with property (t) and (gt) introduced by M. H. M. RACHID in [1] and sprectrale mapping theorem. We will special establish several sufficient and necessary conditions for which f(T) verify the (t) and (gt) as f an analytic function on the T spectrum and see the validity of these results for the semiBrowder operators. Analogously we ask question about the conditions for which the spectral theory hold for generalized a-weyl’s theorem and generalized a-browder’s theorem [18].

Properties (T) and (Gt) for f (T) Type Operators