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Explicit and Unique Construction of Tetrablock Unitary Dilation in a Certain Case

Bhattacharyya, T and Sau, H (2016) Explicit and Unique Construction of Tetrablock Unitary Dilation in a Certain Case. In: COMPLEX ANALYSIS AND OPERATOR THEORY, 10 (4). pp. 749-768.

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Official URL: http://dx.doi.org/10.1007/s11785-015-0472-9

Abstract

Consider the domain E in defined by This is called the tetrablock. This paper constructs explicit boundary normal dilation for a triple (A, B, P) of commuting bounded operators which has as a spectral set. We show that the dilation is minimal and unique under a certain natural condition. As is well-known, uniqueness of minimal dilation usually does not hold good in several variables, e.g., Ando's dilation is known to be not unique, see Li and Timotin (J Funct Anal 154:1-16, 1998). However, in the case of the tetrablock, the third component of the dilation can be chosen in such a way as to ensure uniqueness.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the SPRINGER BASEL AG, PICASSOPLATZ 4, BASEL, 4052, SWITZERLAND
Keywords: Tetrablock; Spectral set; Tetrablock contraction; Tetrablock unitary; Dilation
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 11 May 2016 06:23
Last Modified: 11 May 2016 06:23
URI: http://eprints.iisc.ac.in/id/eprint/53780

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