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Gamma-Unitaries, Dilation and a Natural Example

Bhattacharyya, Tirthankar and Sau, Haripada (2017) Gamma-Unitaries, Dilation and a Natural Example. In: PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 53 (2). pp. 261-285.

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Official URL: http://dx.doi.org/10.4171/PRIMS/53-2-2

Abstract

This note constructs an explicit normal boundary dilation for a commuting pair (S, P) of bounded operators with the symmetrized bidisk Gamma = {(z(1) + z(2), z(1)z(2)) : vertical bar z(1)vertical bar, vertical bar z(2)vertical bar <= 1} as a spectral set. Such explicit dilations have hitherto been constructed only in the unit disk 1 1], the unit bidisk 3] and in the tetrablock 6]. The dilation is minimal and unique under a suitable condition. This paper also contains a natural example of a Gamma-isometry. We compute its associated fundamental operator.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the KYOTO UNIV, PUBLICATIONS RESEARCH INST MATHEMATICAL SCIENCES, OIWAKECHO, KITASHIRAKAWA, SAKYOKU, KYOTO, 606-8502, JAPAN
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 10 Jun 2017 04:41
Last Modified: 10 Jun 2017 04:41
URI: http://eprints.iisc.ac.in/id/eprint/57194

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