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Hilbert空间上混沌的加权移位算子
引用本文:姚玉武,康素玲.Hilbert空间上混沌的加权移位算子[J].合肥学院学报(自然科学版),2009,19(3):8-11.
作者姓名:姚玉武  康素玲
作者单位:合肥学院,数学与物理系,合肥,230601
基金项目:安徽省教育厅自然科研基金项目,合肥学院人才引进基金项目,合肥学院自然科学基金项目 
摘    要:利用权数讨论了加权移位算子T在Hilbert空间l^2(N)上的混沌性质,并给出这些性质在空间l^2(Hn)上的推广;接着讨论了加权移位算子轨道的复杂性,指出一个线性算子的轨道可以和一个紧距离空间上的任意连续函数的轨道具有相同的复杂性.

关 键 词:Hilbert空间  拓扑传递性  加权移位算子  混沌

Chaotic Weighted Shift Operator in Hilbert Spaces
YAO Yu-wu,KANG Su-ling.Chaotic Weighted Shift Operator in Hilbert Spaces[J].Journal of Hefei University :Natural Sciences,2009,19(3):8-11.
Authors:YAO Yu-wu  KANG Su-ling
Institution:Department of Mathematics and Physics;Hefei University;Hefei 230601;China
Abstract:The chaotic weighted shift operator on Hilbert spaces l^2 ( N ) was studied. By using the weight principle, a sufficient condition for a weighted shift operator was obtained, which is chaotic in the sense of Denaney. Let Hn be a separable complex Hilbert space with dimension n ( 1 ≤ n ≤ ∞), the above results on l^2 (Hn ) was generalized. The orbit of linear operator can be as complicated as the orbit of any continuous function on a compact metric space.
Keywords:Hilbert space  topological transitivity  weighted shift operator  chaos  
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