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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/43386/1/A%20review%20of%20some%20works%20in%20the%20theory%20of%20diskcyclic%20operators.pdf |
| _version_ | 1825929352022327296 |
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| author | Bamerni, Nareen Kilicman, Adem Md Noorani, Mohd Salmi |
| author_facet | Bamerni, Nareen Kilicman, Adem Md Noorani, Mohd Salmi |
| author_sort | Bamerni, Nareen |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T08:55:31Z |
| format | Article |
| id | upm.eprints-43386 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:55:31Z |
| publishDate | 2016 |
| publisher | Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Bamerni, Nareen Kilicman, Adem Md Noorani, Mohd Salmi A review of some works in the theory of diskcyclic operators |
| title | 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_short | A review of some works in the theory of diskcyclic operators |
| title_sort | review of some works in the theory of diskcyclic operators |
| url | http://psasir.upm.edu.my/id/eprint/43386/1/A%20review%20of%20some%20works%20in%20the%20theory%20of%20diskcyclic%20operators.pdf |
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