M-hypercyclicity of \(C_0\)-semigroup and SVEP of its generator (Q2063211)

Inspired by the notion of \(M\)-hypercyclic operator on an infinite dimensional separable Banach space \(X\), with \(M\) a non-zero subspace of \(X\), of \textit{B. F. Madore} and \textit{R. A. Martínez-Avendaño} [J. Math. Anal. Appl. 373, No. 2, 502--511 (2011; Zbl 1210.47023)], \textit{A. Tajmouati} et al. introduced the notion of \(M\)-hypercyclicity for \(C_0\)-semigroups of operators in [``On $M$-hypercyclic semigroup'', Int. J. Math. Anal 9, No 9, 417--428 (2015; \url{doi:10.12988/ijma.2015.412397})]. In this paper conditions on the generator \(A\) of a \(C_0\)-semigroup of operators are shown to imply that the semigroup is \(M\)-hypercyclic.