关于Harris算子不可约半群的周边点谱与渐近性
On the peripheral point spectrum and the asymptotic behavior of irreducible semigroups of Harris operators
摘要：
给定巴拿赫格上一个具有序连续范数的正的、不可约的、有界的C_0-半群，证明了当它的一个算子支配一个非平凡紧算子或核算子时，它的生成元的外围点谱是平凡的.对于离散半群，即对于单个算子T的幂，我们证明了某个幂T^k的点谱至多与单位圆相交于1。作为结果，我们分别得到了C_0-半群强收敛和T的幂的子序列强收敛的一个充分条件。
英文摘要：
Given a positive, irreducible and bounded C_0-semigroup on a Banach lattice with order continuous norm, we prove that the peripheral point spectrum of its generator is trivial whenever one of its operators dominates a non-trivial compact or kernel operator. For a discrete semigroup, i.e. for powers of a single operator T, we show that the point spectrum of some power T^k intersects the unit circle at most in 1. As a consequence, we obtain a sufficient condition for strong convergence of the C_0-semigroup and for a subsequence of the powers of T, respectively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
