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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© 1997 Springer Basel AG
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Lomonosov, V., Lyubich, Y., Matsaev, V. (1997). The Duality of Spectral Manifolds and Local Spectral Theory. In: Gohberg, I., Lyubich, Y. (eds) New Results in Operator Theory and Its Applications. Operator Theory: Advances and Applications, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8910-0_14
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DOI: https://doi.org/10.1007/978-3-0348-8910-0_14
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-8910-0
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