International Journal of Mathematics Trends and Technology
Volume 66 | Issue 4 | Year 2020 | Article Id. IJMTT-V66I4P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I4P521
The Set { Tnx:n≥0} is called the orbit of a vector x in a linear topological space X under a linear map T and is denoted by Orb(T,x). If dense orbits exist, T is called a hypercyclic operator. In this paper, a hypercyclic vector is constructed based on the existing sufficient condition for hypercyclicity of an operator T. From a separable Banach space Y and a sequence of real numbers {β(n)}, a sequence space (Y)β is defined and proved that the backward shift operator acting on (Y)β is hypercyclic.
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Varughese Mathew, "On Hypercyclic Operators," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 4, pp. 172-176, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I4P521
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