Construction of operators with prescribed orbits in Fréchet spaces with a continuous norm
- Autores: Angela Ama Albanese
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 109, Nº 1, 2011, págs. 147-160
- Idioma: inglés
- DOI: 10.7146/math.scand.a-15182
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Resumen
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.
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