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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.
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참고문헌 (21)
참고문헌 신청
S. I. Ansari / 1997 / Existance of hypercyclic operatos on topological vector space / J. F. Anal. 148:384~390
F. Bayart / 2009 / Dynamics of linear operators / Cambridge University Press
T. Bermudez / 2004 / On hypercyclicity and supercyclicity criteria / Bull. Austral. Math. Soc. 70(1):45~54
J. A. Conejero / 2010 / Hypercyclic $C_0$ -semigroups generated by Ornstein-Uhlenbeck operators / Mediterr. J. Math. 7(1):101~109
J. A. Conejero / 2005 / Linear transitivity criteria / Topology Appl. 153(5-6):767~773
F. Bayart / 2009 / Dynamics of linear operators / Cambridge University Press
T. Bermudez / 2004 / On hypercyclicity and supercyclicity criteria / Bull. Austral. Math. Soc. 70(1):45~54
J. A. Conejero / 2010 / Hypercyclic
J. A. Conejero / 2005 / Linear transitivity criteria / Topology Appl. 153(5-6):767~773
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