A Review of Some Works in the Theory of Diskcyclic Operators

Nareen Bamerni, Adem Kılıçman, Mohd. Salmi Md. Noorani

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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 (Formula presented.) has a disk orbit under (Formula presented.) that is somewhere dense in (Formula presented.) , then the disk orbit of (Formula presented.) under (Formula presented.) need not be everywhere dense in (Formula presented.). 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 (Formula presented.) over the field of complex numbers if and only if (Formula presented.) or (Formula presented.) . Finally, we give a sufficient condition for the somewhere density disk orbit to be everywhere dense.

Original languageEnglish
Pages (from-to)723-739
Number of pages17
JournalBulletin of the Malaysian Mathematical Sciences Society
Volume39
Issue number2
DOIs
Publication statusPublished - 1 Apr 2016

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Operator
Orbit
Backward Shift
Review
Separable Hilbert Space
Sufficient Conditions
Complex number
Hilbert space
If and only if
Necessary Conditions

Keywords

  • Diskcyclic operators
  • Hypercyclic operators
  • Supercyclic operators
  • Weighted shift operators

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A Review of Some Works in the Theory of Diskcyclic Operators. / Bamerni, Nareen; Kılıçman, Adem; Md. Noorani, Mohd. Salmi.

In: Bulletin of the Malaysian Mathematical Sciences Society, Vol. 39, No. 2, 01.04.2016, p. 723-739.

Research output: Contribution to journalArticle

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