On the direct sum of two bounded linear operators and subspace-hypercyclicity

Volume 8, Issue 1, Article 1 - 2020

Authors: Nareen Bamerni;Adem Kılıc¸man

Copyright © 2020 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

In this paper, we study the relation between subspace-hypercyclicity and the direct sum of two operators. In particular, we show that if the direct sum of two operators is subspace-hypercyclic, then both operators are subspace-hypercyclic; however, the converse is true for a stronger property than subspace-hypercyclicity. Moreover, we prove that if an operator T satisfies subspace-hypercyclic criterion, then T ⊕T is subspace-hypercyclic. However, we show that the converse is true under certain conditions.©2019 All rights reserved.

How To Cite This Article

Nareen Bamerni;Adem Kılıc¸man (2020) On the direct sum of two bounded linear operators and subspace-hypercyclicity
General Letters in Mathematics Vol 8 (1) 1-7
https://doi.org/10.31559/glm2020.8.1.1