UPM Institutional Repository

A review of some works in the theory of diskcyclic operators


Bamerni, Nareen and Kilicman, Adem and Md Noorani, Mohd Salmi (2016) A review of some works in the theory of diskcyclic operators. Bulletin of the Malaysian Mathematical Sciences Society, 39 (2). pp. 723-739. ISSN 0126-6705; ESSN: 2180-4206


In this paper, we give a brief review concerning diskcyclic operators and then we provide some further characterizations of diskcyclic operators on separable Hilbert spaces. In particular, we show that if x∈H has a disk orbit under T that is somewhere dense in H, then the disk orbit of x under T need not be everywhere dense in H. We also show that the inverse and the adjoint of a diskcyclic operator need not be diskcyclic. Moreover, we establish another diskcyclicity criterion and use it to find a necessary and sufficient condition for unilateral backward shifts that are diskcyclic operators. We show that a diskcyclic operator exists on a Hilbert space H over the field of complex numbers if and only if dim(H)=1 or dim(H)=∞ . Finally, we give a sufficient condition for the somewhere density disk orbit to be everywhere dense.

Download File

PDF (Abstract)
A review of some works in the theory of diskcyclic operators.pdf

Download (101kB) | Preview

Additional Metadata

Item Type: Article
Divisions: Faculty of Science
DOI Number: https://doi.org/10.1007/s40840-015-0137-x
Publisher: Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
Keywords: Diskcyclic operators; Hypercyclic operators; Supercyclic operators; Weighted shift operators
Depositing User: Nabilah Mustapa
Date Deposited: 19 May 2016 01:52
Last Modified: 19 May 2016 01:52
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1007/s40840-015-0137-x
URI: http://psasir.upm.edu.my/id/eprint/43386
Statistic Details: View Download Statistic

Actions (login required)

View Item View Item