M-hypercyclicity of C0-semigroup and Svep of its generator

Abstract

Let 𝒯 = (Tt)t≥0 be a C0-semigroup on a separable infinite dimensional Banach space X, with generator A. In this paper, we study the relationship between the single valued extension property of generator A, and the M-hypercyclicity of the C0-semigroup. Specifically, we prove that if A does not have the single valued extension property at λ ∈ iℝ, then there exists a closed subspace M of X, such that the C0-semigroup 𝒯 is M-hypercyclic. As a corollary, we get certain conditions of the generator A, for the C0-semigroup to be M-hypercyclic.

Keywords

• hypercyclicity
• m-hypercyclicity
• c0-semigroup
• svep
• topologically transitive
• 47a19
• 47a10
• 47b48
• 47d03