Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 2, pp 411–427 | Cite as

n-SOT Hypercyclic Linear Maps on Banach Algebra of Operators

  • Narjes Avizeh
  • Hamid RezaeiEmail author
Original Paper


Let B(X) be the algebra of bounded linear operators on a Banach space X. A subset E of B(X) is said to be n-SOT dense in B(X) if for every continuous linear operator \(\Lambda \) from B(X) onto \(X^{(n)}\), the direct sum of n copies of X, \(\Lambda (E)\) is dense in \(X^{(n)}\). We consider the n-SOT hypercyclic continuous linear maps on B(X), namely, those that have orbits that are n-SOT dense in B(X). Some nontrivial examples of such operators are provided and many of their basic properties are investigated. In particular, we show that the left multiplication operator \(L_T\) is 1-SOT hypercyclic if and only if T is hypercyclic on X.


Hypercyclic vector Hypercyclic operator Strong operator topology 

Mathematics Subject Classification

Primary 47A16 Secondary 47B48 



This paper is a part of the N. Avizeh’s doctoral thesis written at Yasouj University under the direction of the H. Rezaei.


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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesYasouj UniversityYasoujIran

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