Geodesic
On orbits for pairs of operators on an infinite-dimensional complex Hilbert space
Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1

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The results presented in this paper are motivated by some of the results obtained by B.~Beauzamy in \cite[Chap. III]{bb1} for a single operator on an infinite-dimensional complex Hilbert space that imply existence of a dense set of vectors with orbits tending strongly to infinity. For the case of invertible operator $T$, one of B.~Beauzamy's results implies that the space actually contains a dense set of vectors for which both the orbits under $T$ and its inverse tend strongly to infinity. We are going to show that this is also true for any suitable pair of operators. 
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     author = {Sonja Man\v{c}evska},
     title = {On orbits for pairs of operators on an infinite-dimensional complex {Hilbert} space},
     journal = {Kragujevac Journal of Mathematics},
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     publisher = {mathdoc},
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Sonja Mančevska. On orbits for pairs of operators on an infinite-dimensional complex Hilbert space. Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1. http://geodesic.mathdoc.fr/item/KJM_2007_30_1_a21/