Abstract
Abstract Let 𝒯 = (Tt ) t ≥0 be a C 0-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 C 0-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 C 0-semigroup 𝒯 is M-hypercyclic. As a corollary, we get certain conditions of the generator A, for the C 0-semigroup to be M-hypercyclic.
Highlights
A continuous linear operator T on a separable Banach space X is called hypercyclic if there exists a vector x ∈ X which, means that orb(T, x) := {Tn x, n ∈ N} is dense in X
We study the relationship between the single valued extension property of generator A, and the M-hypercyclicity of the C -semigroup
Throughout this work, let X be an in nite dimensional separable complex Banach space, M be a non-zero closed subspace of X, and B(X) denote the set of bounded linear operator from X to X
Summary
A continuous linear operator T on a separable Banach space X is called hypercyclic if there exists a vector x ∈ X which, means that orb(T, x) := {Tn x, n ∈ N} is dense in X. Abstract: Let T = (Tt)t≥ be a C -semigroup on a separable in nite dimensional Banach space X, with generator A.
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