in this paper we establish the relation with property (t) and (gt) introduced by M. H. M. RACHID ... more 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 semi-Browder 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].
It is shown that if a bounded linear operator T or its adjoint T* has the single-valued extension... more It is shown that if a bounded linear operator T or its adjoint T* has the single-valued extension property, then generalized Browder's theorem holds for f(T) for every f ∈ H(σ(T)). We establish the spectral theorem for the B-Weyl spectrum which generalizes [15, Theorem 2.1] and we give necessary and sufficient conditions for such operator T to obey generalized Weyl's theorem.
in this paper we establish the relation with property (t) and (gt) introduced by M. H. M. RACHID ... more 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 semi-Browder 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].
It is shown that if a bounded linear operator T or its adjoint T* has the single-valued extension... more It is shown that if a bounded linear operator T or its adjoint T* has the single-valued extension property, then generalized Browder's theorem holds for f(T) for every f ∈ H(σ(T)). We establish the spectral theorem for the B-Weyl spectrum which generalizes [15, Theorem 2.1] and we give necessary and sufficient conditions for such operator T to obey generalized Weyl's theorem.
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