On subspace-supercyclic semigroup
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A $C_{0}$-semigroup $\mathcal{T}=(T_{t})_{t\geq0}$ on a Banach space $X$ is called subspace-supercyclic for a subspace $M,$ if $\mathbb{C}Orb(\mathcal{T},x)\bigcap M = \{\lambda T_{t}x: \lambda\in \mathbb{C}, t\geq0 \}\bigcap M$ 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.
Abstract
A $C_{0}$-semigroup $\mathcal{T}=(T_{t})_{t\geq0}$ on a Banach space $X$ is called subspace-supercyclic for a subspace $M,$ if $\mathbb{C}Orb(\mathcal{T},x)\bigcap M = \{\lambda T_{t}x: \lambda\in \mathbb{C}, t\geq0 \}\bigcap M$ 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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