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arXiv · 1802.03519

On Weak Supercyclicity II

C. S. Kubrusly·B. P. Duggal
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Abstract

This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic, (ii) diagonalizable operators are not weakly l-sequentially supercyclic, and (iii) weak l-sequential supercyclicity is preserved between a unitary operator and its adjoint. On the other hand, weak supercyclicity is investigated for classes of normed-space operators: (iv) the point spectrum of the normed-space adjoint of a power bounded supercyclic operator is either empty or is a singleton in the open unit disk, (v) weak l-sequential supercyclicity coincides with supercyclicity for compact operators, and (vi) every compact weakly l-sequentially supercyclic operator is quasinilpotent.

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C. S. Kubrusly, B. P. Duggal. 2018-02-10. On Weak Supercyclicity II. https://arxiv.org/abs/1802.03519

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