Bhattacharyya, T and Bhowmik, M (2024) A Note on the Dilation of a Certain Family of Tetrablock Contractions. [Book Chapter]
|
PDF
ope_the_adv-app_295_2024.pdf - Published Version Download (186kB) | Preview |
Abstract
We find an explicit tetrablock isometric dilation for every member (Aα,B,P) of a family of tetrablock contractions indexed by a parameter α in the closed unit disc (only the first operator of the tetrablock contraction depends on the parameter). The dilation space is the same for any member of the family. Explicit dilation for the adjoint tetrablock contraction (Aα�,B�,P�) for every member of the family mentioned above is constructed as well. This example is important because it has been claimed in the literature that this example does not have a dilation. Taking cue from this construction and using Toeplitz operators on HD2(DP), we obtain necessary and sufficient conditions for a tetrablock contraction to have a certain type of tetrablock isometric dilation. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
| Item Type: | Book Chapter |
|---|---|
| Publication: | Operator Theory: Advances and Applications |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to author. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 24 May 2024 04:22 |
| Last Modified: | 24 May 2024 04:22 |
| URI: | https://eprints.iisc.ac.in/id/eprint/85064 |
Actions (login required)
 |
View Item |
