Abstract
Let $B$ be a Banach space and $T$ a bounded linear operator on $B.$ A celebrated theorem of Ansari says that whenever $T$ is hypercyclic so is any power $T^n$. We provide a very natural proof of this theorem by building on an approach by Bourdon. We also explore an extension to a non linear setting of a theorem of León-Saavedra and Müller which says that for $\lambda \in \mathbb C$ and $|\lambda|=1$ the operator $\lambda T$ is hypercyclic whenever $T$ is.
Citation
Miguel Marano. Héctor N. Salas. "Maps with dense orbits: Ansari's theorem revisited and the infinite torus." Bull. Belg. Math. Soc. Simon Stevin 16 (3) 481 - 492, August 2009. https://doi.org/10.36045/bbms/1251832374
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