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Weighted Hardy Spaces Over the Unit Ball: The Freely Noncommutative and Commutative Settings Read chapter Read first chapter

2024 | OriginalPaper | Chapter

A Note on the Dilation of a Certain Family of Tetrablock Contractions

Authors : Tirthankar Bhattacharyya, Mainak Bhowmik

Published in: Operator and Matrix Theory, Function Spaces, and Applications

Publisher: Springer Nature Switzerland

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Abstract

We find an explicit tetrablock isometric dilation for every member \((A_\alpha , B, P)\) of a family of tetrablock contractions indexed by a parameter \(\alpha \) 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 \((A_\alpha ^*, B^*, P^*)\) 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 \(H^2_{\mathbb D}(\mathcal D_P)\), we obtain necessary and sufficient conditions for a tetrablock contraction to have a certain type of tetrablock isometric dilation.

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previous chapter Hilbert Transform in the Cartwright–de Branges Space
next chapter Commuting Toeplitz Operators and Moment Maps on Cartan Domains of Type III
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Metadata
Title
A Note on the Dilation of a Certain Family of Tetrablock Contractions
Authors
Tirthankar Bhattacharyya
Mainak Bhowmik
Copyright Year
2024
Book
Operator and Matrix Theory, Function Spaces, and Applications

Print ISBN: 978-3-031-50612-3

Electronic ISBN: 978-3-031-50613-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-50613-0_4

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