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

Authors

  • Angela A. Albanese

DOI:

https://doi.org/10.7146/math.scand.a-15182

Abstract

Let X be a separable, infinite dimensional real or complex Fréchet space admitting a continuous norm. Let {vn: n1} 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: n1}. 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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Published

2011-09-01

How to Cite

Albanese, A. A. (2011). Construction of operators with prescribed orbits in Fréchet spaces with a continuous norm. MATHEMATICA SCANDINAVICA, 109(1), 147–160. https://doi.org/10.7146/math.scand.a-15182

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Articles