Explicit and unique construction of tetrablock unitary dilation in a certain case

Bhattacharyya, T. ; Sau, H. (2016) Explicit and unique construction of tetrablock unitary dilation in a certain case Complex Analysis and Operator Theory, 10 (4). pp. 749-768. ISSN 1661-8254

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Official URL: http://link.springer.com/article/10.1007%2Fs11785-...

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

Abstract

Consider the domain E in C3 defined by E={(a11,a22,detA) : A = (a11,a12 a21,a22) with ||A||<1}. This is called the tetrablock. This paper constructs explicit boundary normal dilation for a triple (A, B, P) of commuting bounded operators which has Ē 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:Article
Source:Copyright of this article belongs to Springer Springer Verlag.
Keywords:Tetrablock; Spectral Set; Tetrablock Contraction; Tetrablock Unitary; Dilation
ID Code:99719
Deposited On:27 Nov 2016 12:49
Last Modified:27 Nov 2016 12:49

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