论文标题
加权偏移的轨道限量点零法律
Zero-one law of orbital limit points for weighted shifts
论文作者
论文摘要
Chan和Seceleanu表明，如果在$ \ ell^p（\ Mathbb {z}）上的加权移动运算符，$ 1 \ leq p <\ infty $，则接纳具有非零极限点的轨道，然后是超循环。我们提供了此结果的新证明，该证明允许将其扩展到非常通用的序列空间。同样，我们表明，在许多序列空间中，具有非零弱依次复发矢量的加权移位具有一组密集的向量。但是$ C_0（\ Mathbb {Z}）上的一个示例表明，这种操作员不一定是超循环。另一方面，我们获得了弱依次的超环体加权移位是超环状的。此外，Chan和Seceleanu的表明，如果伯格曼空间上的伴随乘法算子允许具有非零极限点的轨道，则它是超循环的。我们将此结果扩展到分析功能的非常一般的空间，包括耐寒空间。
Chan and Seceleanu have shown that if a weighted shift operator on $\ell^p(\mathbb{Z})$, $1\leq p<\infty$, admits an orbit with a non-zero limit point then it is hypercyclic. We present a new proof of this result that allows to extend it to very general sequence spaces. In a similar vein we show that, in many sequence spaces, a weighted shift with a non-zero weakly sequentially recurrent vector has a dense set of such vectors; but an example on $c_0(\mathbb{Z})$ shows that such an operator is not necessarily hypercyclic. On the other hand, we obtain that weakly sequentially hypercyclic weighted shifts are hypercyclic. Chan and Seceleanu have moreover shown that if an adjoint multiplication operator on a Bergman space admits an orbit with a non-zero limit point then it is hypercyclic. We extend this result to very general spaces of analytic functions, including the Hardy spaces.
