Abstract
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.
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© 2007 Birkhäuser Verlag AG, P.O. Box 133, CH-4010 Basel, Switzerland
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(2007). Orbits and Capacity. In: Spectral Theory of Linear Operators. Operator Theory: Advances and Applications, vol 139. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8265-0_5
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DOI: https://doi.org/10.1007/978-3-7643-8265-0_5
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8264-3
Online ISBN: 978-3-7643-8265-0
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