A C0-semigroup T = (Tt) t≥0 on an infinite-dimensional separable complex Banach space X is called subspace-hypercyclic for a subspace M, if Orb(T , x) M is dense in M for a vector x ∈ M . In this paper, we localize the notion of M-extended semigroup(resp.M-extended semigroup mixing) limit set of x under T and We give sufficient conditions of being M -hypercyclic for this semigroup. Then by this result, we prove that (T −1 t ) t≥0 is a M -hypercyclic. This result is an answer of the question of B. F. Madore and R. A. Martnez-Avendano for C0-semigroup.
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