| This dissertation addresses some of the geometric properties of orbits of integral operators on the Banach spaces C[0, 1] and Lp[0, 1]. It will be shown that, under very general conditions on the starting element, an orbit of the Volterra operator cannot be a Schauder basis for its closed linear span. However, lacunary subsequences of the orbit will be seen to be Schauder bases for their closed linear span. Bounds on the norm of the iterates and a monotonicity result for a certain class of functions will be established. Moreover, exact asymptotic constants arising from the analysis will be exhibited. |
