Abstract
Abstract In this paper, we prove our main result that the Li-Yorke chaotic eigen set of a positive integer multiple of the backward shift operator on ℓ2 () is a disk in the complex plane and the union of such Li-Yorke chaotic eigen set’s is the whole complex plane .
Highlights
In this paper, we prove our main result that the Li-Yorke chaotic eigen set of a positive integer multiple of the backward shift operator on (N) is a disk in the complex plane C and the union of such Li-Yorke chaotic eigen set’s is the whole complex plane C
The concept of Li-Yorke chaoticity of a continuous mapping in a topological dynamical system and the concept of irregular vectors of Hilbert space operators are well known in Chaos theory and Operator theory respectively
We have shown that for any λ ∈ (n + )D, nT − λI is Li-Yorke chaotic and for any λ ∉ (n + )D, nT − λI is not Li-Yorke chaotic, which proves that LY(nT) = (n + )D
Summary
The concept of Li-Yorke chaoticity of a continuous mapping in a topological dynamical system and the concept of irregular vectors of Hilbert space operators are well known in Chaos theory and Operator theory respectively (see [1], [2], [3], [6], [11], [13], [14]). Abstract: In this paper, we prove our main result that the Li-Yorke chaotic eigen set of a positive integer multiple of the backward shift operator on (N) is a disk in the complex plane C and the union of such Li-Yorke chaotic eigen set’s is the whole complex plane C. We made an attempt to link these two concepts together and introduce the Li-Yoke chaoticity of an operator in a separable complex Hilbert space.
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