On weak supercyclicity II

Kubrusly, Carlos S. ; Duggal, Bhagwati P.

Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 371-386

Abstract (VO)

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.

Détail

DOI : 10.21136/CMJ.2018.0457-16

Classification : 47A16, 47B15
Keywords: supercyclic operator; weakly supercyclic operator; weakly $l$-sequentially supercyclic operator

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