A Note on Topological and Strict Transitivity

作者：Ansari Mohammad; Hedayatian Karim; Robati Bahram Khani^*; Moradi Abbas

来源：Iranian Journal of Science and Technology Transaction A-Science, 2018, 42(A1): 59-64.

DOI：10.1007/s40995-017-0325-7

• Hypercyclic
• Supercyclic
• Topologically transitive
• Strictly transitive

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.

• 出版日期2018-3