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Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class denoted by l-*-A, of operators satisfying T*|T2|T ≥ T*|T*|2T, and we prove the basic properties of these operators. Using these results, we also prove that if T or T* ∈ l-*-A, then w(f(T)) = f(w(T)), σea(f(T)) = f(σea(T)) for every f ∈ H(σ(T)), where H(σ(T)) denotes the set of all analytic functions...
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