English

On Weak Supercyclicity II

Functional Analysis 2021-01-29 v3

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.

Keywords

Cite

@article{arxiv.1802.03519,
  title  = {On Weak Supercyclicity II},
  author = {C. S. Kubrusly and B. P. Duggal},
  journal= {arXiv preprint arXiv:1802.03519},
  year   = {2021}
}
R2 v1 2026-06-23T00:17:44.823Z