Orbits, weak orbits and local capacity of operators

Let T be an operator on a Banach space X. We give a survey of results concerning orbits {T(n)x : n = 0,1....} and weak orbits {[T(n)x, x*] : n = 0, 1,...} of T where x is an element of X and x* is an element of X*- Further we study the local capacity of operators and prove that there is a residual set of points x is an element of X with the property that the local capacity cap (T, x) is equal to the global capacity cap T. This is an analogy to the corresponding result for the local spectral radius.