Refaad for Studies, Research and Developement
On the direct sum of two bounded linear operators and subspace-hypercyclicity
2519-9269 (Print)
2519-9277 (Online)
Volume 8
Issue 1
2020
March
0
On the direct sum of two bounded linear operators and subspace-hypercyclicity
1
7
English
Nareen BamerniDepartment of Mathematics, University of Duhok, Kurdistan Region, Iraqnareen_bamerni@yahoo.com
Adem Kılıc¸manDepartment of Mathematics, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysiaakilicman@yahoo.com
10.31559/glm2020.8.1.1
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.
Hypercyclic operators; Direct sums
http://www.refaad.com/views/GLM/811.html
http://www.refaad.com/Files/GLM/GLM-8-1-1.pdf