Orbits and Capacity
Let T be an operator on a Banach space X. By an orbit of T we mean a sequence (Tnx) n ∞ =0, where x ∈ X is a fixed vector. This notion, which originated in the theory of dynamical systems, is closely related to the concepts of local spectral radius and capacity of an operator. Further motivations come from stability problems of semigroups of operators and the invariant subspace problem.
KeywordsBanach Space Invariant Subspace Spectral Radius Banach Algebra Dense Subset
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