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: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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 http://psasir.upm.edu.my/id/eprint/43386/ http://link.springer.com/article/10.1007%2Fs40840-015-0137-x |
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| Summary: | 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. |
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