Occasionally attracting compact sets and compact-supercyclicity

Details Occasionally attracting compact sets and compact-supercyclicity Occasionally attracting compact sets and compact-supercyclicity

2006-04-07

arxiv.org/abs/math/0604159v1

Mathematics

Functional Analysis

5 pages

Scientific paper

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 $\liminf_n \rho(T^n x, K)=0$ then there exists attracting finite-dimensional subspace $L$ (for each x in X $\lim_n \rho(T^n x, L)=0$. 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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