Maps with dense orbits: Ansari's theorem revisited and the infinite
torus

Marano, Miguel; Salas, Héctor N.

Maps with dense orbits: Ansari's theorem revisited and the infinite torus

Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, p. 481-492 / Harvested from Project Euclid

Résumé

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.

Publié le : 2009-08-15
Classification: Hypercyclic operators, dense orbits, transitive maps, measurable-preserving maps, ergodic maps, infinite torus, 47A16, 37A99, 22D40

@article{1251832374,
     author = {Marano, Miguel and Salas, H\'ector N.},
     title = {Maps with dense orbits: Ansari's theorem revisited and the infinite
torus},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {16},
     number = {1},
     year = {2009},
     pages = { 481-492},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1251832374}
}

Marano, Miguel; Salas, Héctor N. Maps with dense orbits: Ansari's theorem revisited and the infinite
torus. Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, pp.  481-492. http://gdmltest.u-ga.fr/item/1251832374/