Annals of Functional Analysis

Weighted backward shift operators with invariant distributionally scrambled subsets

Xinxing Wu, Lidong Wang, and Guanrong Chen

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Abstract

We obtain a sufficient condition to ensure that weighted backward shift operators on Köthe sequence spaces λp(A) admit an invariant distributionally ε-scrambled subset for any 0<ε<diamλp(A). In particular, every Devaney chaotic weighted backward shift operator on λp(A) supports such a subset.

Article information

Source
Ann. Funct. Anal., Volume 8, Number 2 (2017), 199-210.

Dates
Received: 18 March 2016
Accepted: 18 August 2016
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1485831762

Digital Object Identifier
doi:10.1215/20088752-3802705

Mathematical Reviews number (MathSciNet)
MR3603775

Zentralblatt MATH identifier
1373.47027

Subjects
Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators
Secondary: 47A15: Invariant subspaces [See also 47A46] 47A16: Cyclic vectors, hypercyclic and chaotic operators

Keywords
weighted backward shift distributional chaos invariant subset Köthe sequence space

Citation

Wu, Xinxing; Wang, Lidong; Chen, Guanrong. Weighted backward shift operators with invariant distributionally scrambled subsets. Ann. Funct. Anal. 8 (2017), no. 2, 199--210. doi:10.1215/20088752-3802705. https://projecteuclid.org/euclid.afa/1485831762


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