Abstract
Let \(X\) be a normed linear space and \(L(X)\) be the algebra of continuous linear operators on \(X\). We give a necessary condition for topological transitivity of subsets of \(L(X)\) which gives a necessary condition for hypercyclicity and supercyclicity of a single operator on \(X\). Also, we prove the strict transitivity of some particular families of operators on locally convex spaces and Hilbert spaces.
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Ansari, M., Hedayatian, K., Robati, B.K. et al. A Note on Topological and Strict Transitivity. Iran J Sci Technol Trans Sci 42, 59–64 (2018). https://doi.org/10.1007/s40995-017-0325-7
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DOI: https://doi.org/10.1007/s40995-017-0325-7