Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 68, No. 2, pp. 371-386, 2018

On weak supercyclicity II

Carlos S. Kubrusly, Bhagwati P. Duggal

Received August 28, 2016. First published February 2, 2018.

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: supercyclic operator; weakly supercyclic operator; weakly $l$-sequentially supercyclic operator

Classification MSC: 47A16, 47B15

DOI: 10.21136/CMJ.2018.0457-16

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Carlos S. Kubrusly, Department of Applied Mathematics, Mathematics Institute, Federal University of Rio de Janeiro, Av. Pedro Calmon, 550 - Cidade Universitária, Rio de Janeiro, 21941-909, Brazil, e-mail: carloskubrusly@gmail.com; Bhagwati P. Duggal, 8 Redwood Grove, Northfield Avenue, Ealing, London W5 4SZ, United Kingdom, e-mail: bpduggal@yahoo.co.uk

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