Abstract
Let T be an arbitrary linear bounded operator on a complex Banach space B. As usual, we denote by ρ(T) the resolvent set of T, i.e., ρ(T) is the set of λ ∈ C such that the resolvent R λ(T) = (T - λI)y-1 exists in the algebra of all linear bounded operators on B. This set is open and R λ(T) is an analytic operator function on it. The spectrum σ(T) = C/ρ(T) is compact.
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