Supercyclic sequences of differential operators. (English) Zbl 1093.47006
If \(T\) is an operator on a linear topological space \(X\) on \(K\) (real or complex numbers), then a vector \(x \in X\) is called supercyclic for \(T\) whenever its projective orbit \(\{\lambda T^{n}x : \lambda \in K,\;n=1,2,3,\dots\}\) is dense in \(X\). The operator \(T\) is called supercyclic if there is some supercyclic vector for \(T\).
In the paper under review, the authors introduce a criterion to be densely supercyclic for a sequence \((T_n)\) of operators on a Baire metrizable separable linear topological space \(X\). Among other results, they also give necessary and sufficient conditions for a sequence of differential operators to be supercyclic or c-hypercyclic.
In the paper under review, the authors introduce a criterion to be densely supercyclic for a sequence \((T_n)\) of operators on a Baire metrizable separable linear topological space \(X\). Among other results, they also give necessary and sufficient conditions for a sequence of differential operators to be supercyclic or c-hypercyclic.
Reviewer: Ömer Gök (Istanbul)
MSC:
47A16 | Cyclic vectors, hypercyclic and chaotic operators |
30H05 | Spaces of bounded analytic functions of one complex variable |
32A07 | Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010) |
47B38 | Linear operators on function spaces (general) |
47E05 | General theory of ordinary differential operators |