Abstract
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.
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Acknowledgements
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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Communicated by Ali Abkar.
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Avizeh, N., Rezaei, H. n-SOT Hypercyclic Linear Maps on Banach Algebra of Operators. Bull. Iran. Math. Soc. 45, 411–427 (2019). https://doi.org/10.1007/s41980-018-0140-8
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DOI: https://doi.org/10.1007/s41980-018-0140-8