Article ID Journal Published Year Pages File Type
4622288 Journal of Mathematical Analysis and Applications 2007 6 Pages PDF
Abstract

If (Tt)t⩾0(Tt)t⩾0 is a bounded C0C0-semigroup in a Banach space X   and there exists a compact subset K⊆XK⊆X such thatlim inft→∞ρ(Ttx,K)=0(∀x∈X,‖x‖⩽1), then there exists a finite-dimensional subspace L⊆XL⊆X such thatlimt→∞ρ(Ttx,L)=0(∀x∈X).If T:X→X (X   is real or complex) is supercyclic and (‖Tn‖)n(‖Tn‖)n is bounded then (Tnx)n(Tnx)n vanishes for every x∈Xx∈X.We define the “compact-supercyclicity.” If dimX=∞dimX=∞ then X has no compact-supercyclic isometries.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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