Resumen de Construction of operators with prescribed orbits in Fréchet spaces with a continuous norm

Angela Ama Albanese

• Let X be a separable, infinite dimensional real or complex Fréchet space admitting a continuous norm. Let {vn: 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 v1 under T is exactly the set {vn: 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.