Hilbert Jamison序列与刚性动力系统
Hilbertian Jamison sequences and rigid dynamical systems
摘要：
一个严格递增的正整数序列（n_k）称为Hilbert Jamison序列，如果对可分希尔伯特空间上的任何有界算子T，使得||T^{n_k}||是有限的，T的模1的特征值的集合至多是可数的。我们首先给出了这样的序列的一个完整的特征。然后我们转向研究测度空间上弱混合动力系统的刚性序列（n_k），并给出序列是刚性序列的各种条件，其中一些条件与Jamison条件密切相关。我们得到了我们的方式的拓扑刚性和一致刚性序列的线性动力系统的一个完整的特征，我们在这个框架内构建的例子动力系统，这是弱混合在测度论意义上和一致刚性。
英文摘要：
A strictly increasing sequence (n_k) of positive integers is said to be a Hilbertian Jamison sequence if for any bounded operator T on a separable Hilbert space such that the supremum over k of the norms ||T^{n_k}|| is finite, the set of eigenvalues of modulus 1 of T is at most countable. We first give a complete characterization of such sequences. We then turn to the study of rigidity sequences (n_k) for weakly mixing dynamical systems on measure spaces, and give various conditions, some of which are closely related to the Jamison condition, for a sequence to be a rigidity sequence. We obtain on our way a complete characterization of topological rigidity and uniform rigidity sequences for linear dynamical systems, and we construct in this framework examples of dynamical systems which are both weakly mixing in the measure-theoretic sense and uniformly rigid.
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