Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON SUBSPACE-SUPERCYCLIC SEMIGROUP

  • El Berrag, Mohammed (Sidi Mohamed Ben Abdellah University Laboratory of Mathematical Analysis and Applications Faculty of Sciences Dhar El Mahraz Fez) ;
  • Tajmouati, Abdelaziz (Sidi Mohamed Ben Abdellah University Laboratory of Mathematical Analysis and Applications Faculty of Sciences Dhar El Mahraz Fez)
  • Received : 2017.02.14
  • Accepted : 2017.04.26
  • Published : 2018.01.31
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Abstract

A $C_0$-semigroup ${\tau}=(T_t)_{t{\geq}0}$ on a Banach space X is called subspace-supercyclic for a subspace M, if $\mathbb{C}Orb({\tau},x){\bigcap}M=\{{\lambda}T_tx\;:\;{\lambda}{\in}\mathbb{C},\;t{\geq}0\}{\bigcap}M$ is dense in M for a vector $x{\in}M$. In this paper we characterize the notion of subspace-supercyclic $C_0$-semigroup. At the same time, we also provide a subspace-supercyclicity criterion $C_0$-semigroup and offer two equivalent conditions of this criterion.

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