Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectr...Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectrum of T and T={λ∈C:|λ|=1},and that there is a non-hypercyclic,sensitive system(X,T) which is not syndetically sensitive.We also show that there is a transitively sensitive system(X,T) which is mean sensitive but not multi-transitively sensitive.展开更多
文摘Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectrum of T and T={λ∈C:|λ|=1},and that there is a non-hypercyclic,sensitive system(X,T) which is not syndetically sensitive.We also show that there is a transitively sensitive system(X,T) which is mean sensitive but not multi-transitively sensitive.
