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http://dx.doi.org/10.4134/JKMS.j190850

STRONG HYPERCYCLICITY OF BANACH SPACE OPERATORS  

Ansari, Mohammad (Department of Mathematics Azad University of Gachsaran)
Hedayatian, Karim (Department of Mathematics Shiraz University)
Khani-Robati, Bahram (Department of Mathematics Shiraz University)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.1, 2021 , pp. 91-107 More about this Journal
Abstract
A bounded linear operator T on a separable infinite dimensional Banach space X is called strongly hypercyclic if $$X{\backslash}\{0\}{\subseteq}{\bigcup_{n=0}^{\infty}}T^n(U)$$ for all nonempty open sets U ⊆ X. We show that if T is strongly hypercyclic, then so are Tn and cT for every n ≥ 2 and each unimodular complex number c. These results are similar to the well known Ansari and León-Müller theorems for hypercyclic operators. We give some results concerning multiplication operators and weighted composition operators. We also present a result about the invariant subset problem.
Keywords
Strongly hypercyclic; strongly supercyclic; hypertransitive; invariant subset;
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