HYPERCYCLIC OPERATORS, MIXING OPERATORS AND THE BOUNDED STEPS PROBLEM

By S. Grivaux. 2005

103 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/618f5551dd25ee2dfe71de83b310507ea593d5b1

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Citations in the corpus

A new class of frequently hypercyclic operators (2010, background): “−2))∩V2 6= ∅}. Since T is hypercyclic, E2 is non-empty. But we can actually say more about E2: as T is hypercyclic and has spanning unimodular eigenvectors, T satisﬁes the Hypercyclicity Criterion by [14]. Hence for any r ≥ 1, the operator Tr which is a direct sum of r copies of T on the direct sum ”
Szemeredi's theorem, frequent hypercyclicity and multiple recurrence (2010, methodology): “In fact, as observed by Grivaux in (Grivaux, 2005), I + T is even mixing.”
HYPONORMAL OPERATORS, WEIGHTED SHIFTS AND WEAK FORMS OF SUPERCYCLICITY (2006, background): “In the hypercyclicity setting, this problem is studied in [7], where it is proved that if T is a hypercyclic operator, then T ⊕ T is cyclic if and only if T satisfies the so-called hypercyclicity criterion (we refer the reader to [7] for the relevant definitions).”
Linear chaos and frequent hypercyclicity (2014, background): “On the other hand, thanks to Bonet and Peris [16], we know that every separable infinite-dimensional Fréchet space supports a hypercyclic operator and even a mixing operator [23].”
A short proof of existence of disjoint hypercyclic operators (2010, background): “Grivaux [7] observed that hypercyclic operators T constructed in [6] are in fact mixing and therefore hereditarily hypercyclic.”
On the spectrum of frequently hypercyclic operators (2008, background): “ by the following chain of results. Ansari [1] and BernalGonza´les [6] showed independently that for any separable inﬁnite dimensional Banach space X there is a hypercyclic operator T ∈ L(X). Grivaux [15] proved that there is a mixing operator on any separable inﬁnite dimensional Banach space. Final”