A note on topological and strict transitivity

Articles in Press

Document Type : Regular Paper

Authors

1 Shiraz university

2 Shiraz University

Abstract

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.
Key words and phrases: hypercyclic, supercyclic, topologically transitive, strictly transitive

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Iranian Journal of Science

Articles in Press, Accepted Manuscript
Available Online from 18 June 2016

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