Simultaneous chaotic extensions for general operators on a Hilbert subspace

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• 作者：Kit C. Chan^a ; ^{kchan@bgsu.edu} ; Leonardo Pinheiro^b ; ^{lpinheiro@ric.edu}
• 关键词：Hilbert space ; Chaotic operator ; Hypercyclic operator ; Extension ; Infinite codimension
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：937-967
• 全文大小：689 K
• 卷排序：448

文摘

For an infinite-codimensional closed subspace M of a separable Hilbert space H  , we show that every bounded linear operator A:M→HA:M→H has a chaotic extension T:H→HT:H→H. As a generalization of this result, we further show that for any uniformly bounded sequence of linear operators An:M→HAn:M→H, there exists a bounded linear operator V:M⊥→HV:M⊥→H on the orthogonal complement M⊥M⊥ of M   that simultaneously extends all operators AnAn to chaotic operators An+V:H→HAn+V:H→H.