Construction of operators with prescribed orbits in Fréchet spaces with a continuous norm - Albanese, Angela A. (MATHEMATICA SCANDINAVICA, 2011)
Let X be a separable, infinite dimensional real or complex Fréchet space admitting a continuous norm. Let {v_n: n≥ 1} be a dense set of linearly independent vectors of X. We show that there exists a continuous linear operator T on X such that the orbit of v_1 under T is exactly the set {v_n: n≥ 1}. Thus, we extend a result of Grivaux for Banach spaces to the setting of non-normable Fréchet spaces with a continuous norm. We also provide some consequences of the main result.