论文标题
有条理的子序列和弱动力学
Boundedly Spaced Subsequences and Weak Dynamics
论文作者
论文摘要
本文的目的是为希尔伯特空间收缩而弱的超级环境表征，这与统一操作员的超级环境相当。确切地说，根据引理3.1 $。$。定理4.1的主要结果是根据有限间隔的子序列进行调查的，定理的主要结果是弱的l- sequarly sequarlyscyclic单一操作员$ u \！$，它们在范围内的范围序列分为$ \^u^^u^^^^y^y^y \^^y \^的表现较弱，它们的弱不稳定。对于弱不稳定的统一操作员的超级\ - 循环性等同于表征任何形式的弱超级环境，用于nagy \ c s- langer分解后弱不稳定的收缩。
The purpose of this paper is to characterize weak supercyclicity for Hilbert-space contractions, which is shown to be equivalent to characterizing weak supercyclicity for unitary operators$.$ This is naturally motivated by an open question that asks whether every weakly supercyclic power bounded operator is weakly stable (which in turn is naturally motivated by a result that asserts that every supercyclic power bounded operator is strongly stable)$.$ Precisely, weakly supercyclicity is investigated in light of boundedly spaced subsequences as discussed in Lemma 3.1$.$ The main result in Theorem 4.1 characterizes weakly l-sequentially supercyclic unitary operators $U\!$ that are weakly unstable in terms of boundedly spaced subsequences of the power sequence $\{U^n\}.$ Remark 4.1 shows that characterizing any form of weak super\-cyclicity for weakly unstable unitary operators is equivalent to characterizing any form of weak supercyclicity for weakly unstable contractions after the Nagy--Foia\c s--Langer decomposition.
