The Duality of Spectral Manifolds and Local Spectral Theory
Victor I. Lomonosov, Yu. I. Lyubich, V. Matsaev · Birkhäuser Basel eBooks · 1997
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.