Orbits and Capacity

Part of the Operator Theory: Advances and Applications book series (OT, volume 139)


Let T be an operator on a Banach space X. By an orbit of T we mean a sequence (Tnx) n =0, where xX 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.


Banach Space Invariant Subspace Spectral Radius Banach Algebra Dense Subset 
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© Birkhäuser Verlag AG, P.O. Box 133, CH-4010 Basel, Switzerland 2007

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