Occasionally attracting compact sets and compact-supercyclicity

K. Storozhuk

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arXiv · math/0604159

Occasionally attracting compact sets and compact-supercyclicity

K. Storozhuk

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Abstract

Let $X$ be a real or complex Banach space and $T_t:X\to X$ is a power bounded operator (or a $C_0$-semigroup). If there exists a "occasionally" attracting compact subset K (for each x$ in unit ball $\liminf_n ρ(T^n x, K)=0$ then there exists attracting finite-dimensional subspace $L$ (for each x in X $\lim_n ρ(T^n x, L)=0$. Also we define the compact-supercyclicity. Each infinity-dimentional $X$ has no compact-supercyclic isometries. If $T$ is a supercyclic and power bounded that $T^nx$ vanishes for each $x$.

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BibTeX RIS

K. Storozhuk. 2006-04-07. Occasionally attracting compact sets and compact-supercyclicity. https://arxiv.org/abs/math/0604159

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