arXiv subjects

K. Storozhuk

Publications and source records attributed to K. Storozhuk.

2 recordsLinked to original sources

arXiv2006

Occasionally attracting compact sets and compact-supercyclicity

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 $x$.

math.FA↗

arXiv2004

Asymptotical behavior of subspaces under action of asymptotically finite-dimensional semigroups of operators

We study a semigroup $ϕ$ of linear operators acting on a Banach space $X$ which satisfies the condition $\codim X_0<\infty$, where $X_0=\{x\in X \mid ϕ_t(x)\underset{t\to\infty}\longrightarrow 0\}.$ We show that $X_0$ is closed under these conditions. We establish some properties concerning the asymptotic behavior of subspaces which complement $X_0$ in $X$.

math.FA↗