2014/10/10 by Nareen Bamerni, Adem Kılıçman, Bamerni, Nareen +3
Mathematics · #47A16 #Algebraic and Geometric Analysis #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:47A16
paper · pdf · doi:10.48550/arxiv.1410.2700
To appear in bull. malays. math. sci. soc
openalex publication_date 2014/10/10 · arxiv created 2015/01/15 · arxiv updated 2015/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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∈ \mathcal H has a disk orbit under T that is somewhere dense in \mathcal H then the disk orbit of x under T need not be everywhere dense in \mathcal 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 \mathcal H over the field of complex numbers if and only if dim(\mathcal H)=1 or dim(\mathcal H)=∞ . Finally we give a sufficient condition for the somewhere density disk orbit to be everywhere dense.