Affiliation:
1. Abdelmalek Essaadi University - Faculty of Sciences and Technology - Al Hoceima , Morocco
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.
Subject
Applied Mathematics,Analysis
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