publication . Article . Preprint . 2020

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

Nareen Bamerni; Adem Kılıc¸man;
Open Access
  • Published: 04 May 2020 Journal: General Letters in Mathematics, volume 8, pages 1-7 (issn: 2519-9269, eissn: 2519-9277, Copyright policy)
  • Publisher: Refaad for Studies and Research
Abstract
AbstractIn this paper, we show that if the direct sum of two opera-tors is subspace-hypercyclic (satisfies subspace hypercyclic crite-rion), then both operators are subspace-hypercyclic (satisfy sub-space hypercyclic criterion). Moreover, if an operator T satisfiessubspace-hypercyclic criterion, then so T⊕T does. Also, we obtainthat under certain conditions, if T ⊕T is hypercyclic then T satis-fies subspace-hypercyclic criterion and, the subspace-hypercyclicoperators satisfy subspace-hypercyclic criterion which gives the“subspace-hypercyclic” analogue of Theorem 2.3. (in Hereditar-ily hypercyclic operators. J. Funct. Anal., 167:94–112, 1999 by P.B´es and A. Peris)....
Subjects
free text keywords: hypercyclic operators, direct sums, Mathematics - Functional Analysis, Subspace topology, Linear operators, Hypercyclic operator, Mathematics, Bounded operator, Banach space, Operator (computer programming), Pure mathematics, Bounded function, Direct sum, lcsh:Mathematics, lcsh:QA1-939
Related Organizations

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[12] T. Sorayya, Meysam A. On subspace-transitive operators, International Journal of Pure and Applied Mathematics. 84 (2013), 643-649.

[13] T. Sorayya, Moosapoor. M, Subspace-Chaotic Operators and Subspace-Weakly Mixing Operators, International Journal of Pure and Applied Mathematics.78, No. 6 (2012), 879-885.

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