publication . Preprint . Article . 2020

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

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• Published: 04 May 2020
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)....
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free text keywords: Mathematics - Functional Analysis, hypercyclic operators, direct sums, lcsh:Mathematics, lcsh:QA1-939, Subspace topology, Linear operators, Hypercyclic operator, Mathematics, Bounded operator, Banach space, Operator (computer programming), Pure mathematics, Bounded function, Direct sum
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