# Occasionally attracting compact sets and compact-supercyclicity

Source: [Occasionally attracting compact sets and compact-supercyclicity](<https://www.sota2.com/research/paper/68fa4d401e209131ce953447>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T09:13:36.256Z

Authors: K. Storozhuk

Published: 2006-04-07T06:53:23.000Z

## 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 $\\liminf\_n \\rho(T^n x, K)=0$ 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0604159>)

[PDF](<https://arxiv.org/pdf/math/0604159.pdf>)