Note on epsilon-cyclic operator

Muammer Badree  Abed; Zeana Zaki  Jamil

doi:10.30526/39.1.4224

Authors

Muammer Badree Abed Department of mathematics, College of Science, University of Baghdad https://orcid.org/0009-0002-4668-2732
Zeana Zaki Jamil Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0001-9123-5849

DOI:

https://doi.org/10.30526/39.1.4224

Keywords:

Keywords:-cyclic operator, hypercyclic operator, diskcyclic operators, -hypercyclic operator, -diskcyclic operator.

Abstract

In this paper, we investigated the concept of ε-diskcyclic operators on a separable infinite-dimensional Hilbert space . A bounded linear operator is called -diskcyclic if there exists a vector in such that its disk orbit visits every cone of aperture . That is, for every non-zero vector in , there exist in where and in such that . Such a vector is then called an ε-diskcyclic vector for .

We established several properties of ε-diskcyclic operators. In particular, we showed that every -diskcyclic operator is cyclic. Moreover, we examined the relationship between ε-diskcyclic vectors of and eigenvectors of the adjoint operator that cannot be orthogonal to each other. We also proved that if is a bounded linear operator on ; , then the direct sum is -diskcyclic provided each is -diskcyclic. Finally, we presented a criterion for determining -diskcyclicity

Author Biographies

Muammer Badree Abed, Department of mathematics, College of Science, University of Baghdad

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Zeana Zaki Jamil, Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

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