Abstract
LetT be an operator on a Banach spaceX. We give a survey of results concerning orbits {T n x:n=0,1,...} and weak orbits {〈T n x,x *〉:n=0,1,...} ofT wherex∈X andx *∈X *. Further we study the local capacity of operators and prove that there is a residual set of pointsx∈X with the property that the local capacity cap(T, x) is equal to the global capacity capT. This is an analogy to the corresponding result for the local spectral radius.
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The research was supported by the grant No. A1019801 of AV ČR.
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Müller, V. Orbits, weak orbits and local capacity of operators. Integr equ oper theory 41, 230–253 (2001). https://doi.org/10.1007/BF01295307
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DOI: https://doi.org/10.1007/BF01295307