The Duality of Spectral Manifolds and Local Spectral Theory
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.
KeywordsLinear Subspace Complex Banach Space Linear Continuous Functional Spectral Subspace Invariant Closed Subspace
Unable to display preview. Download preview PDF.
- 2.Golojoara I. and Foias C,: Theory of Generalized Spectral Operators, Gordon & Breach, N.Y. 1968.Google Scholar
- 4.Lange R. and Wang S.: New approaches in spectral decomposition. Contemp. Math., 128, AMS, 1992.Google Scholar
- 5.Lomonosov V.I.: Some questions of the theory of invariant subspaces, Ph.D. Thesis, Kharkov, 1973.Google Scholar