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A review of some works in the theory of diskcyclic operators

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 nee...

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Main Authors: Bamerni, Nareen, Kilicman, Adem, Md Noorani, Mohd Salmi
Format: Article
Language:English
Published: Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2016
Online Access:http://psasir.upm.edu.my/id/eprint/43386/1/A%20review%20of%20some%20works%20in%20the%20theory%20of%20diskcyclic%20operators.pdf
http://psasir.upm.edu.my/id/eprint/43386/
http://link.springer.com/article/10.1007%2Fs40840-015-0137-x
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spelling my.upm.eprints.433862016-05-19T01:52:28Z http://psasir.upm.edu.my/id/eprint/43386/ A review of some works in the theory of diskcyclic operators Bamerni, Nareen Kilicman, Adem Md Noorani, Mohd Salmi 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. Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/43386/1/A%20review%20of%20some%20works%20in%20the%20theory%20of%20diskcyclic%20operators.pdf 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 http://link.springer.com/article/10.1007%2Fs40840-015-0137-x 10.1007/s40840-015-0137-x
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description 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.
format Article
author Bamerni, Nareen
Kilicman, Adem
Md Noorani, Mohd Salmi
spellingShingle Bamerni, Nareen
Kilicman, Adem
Md Noorani, Mohd Salmi
A review of some works in the theory of diskcyclic operators
author_facet Bamerni, Nareen
Kilicman, Adem
Md Noorani, Mohd Salmi
author_sort Bamerni, Nareen
title A review of some works in the theory of diskcyclic operators
title_short A review of some works in the theory of diskcyclic operators
title_full A review of some works in the theory of diskcyclic operators
title_fullStr A review of some works in the theory of diskcyclic operators
title_full_unstemmed A review of some works in the theory of diskcyclic operators
title_sort review of some works in the theory of diskcyclic operators
publisher Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/43386/1/A%20review%20of%20some%20works%20in%20the%20theory%20of%20diskcyclic%20operators.pdf
http://psasir.upm.edu.my/id/eprint/43386/
http://link.springer.com/article/10.1007%2Fs40840-015-0137-x
_version_ 1643833551192326144
score 13.211869

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