Springer Iranian Journal of Science 2731-8095 Articles in Press 2016 06 18 A note on topological and strict transitivity 3724 10.22099/ijsts.2016.3724 EN Bahram Khani Robati Shiraz university Mohammad Ansari Shiraz University Karim Hedayatian Shiraz University Abbas Moradi Shiraz University Journal Article 2015 10 20 Abstract<br>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.<br>Key words and phrases: hypercyclic, supercyclic, topologically transitive, strictly transitive