-Unitaries, Dilation and a Natural Example

  • Tirthankar Bhattacharyya

    Indian Institute of Science, Bangalore, India
  • Haripada Sau

    Indian Institute of Science, Bangalore, India


This note constructs an explicit normal boundary dilation for a commuting pair of bounded operators with the symmetrized bidisk

as a spectral set. Such explicit dilations had hitherto been constructed only in the unit disk [11], 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 -isometry. We compute its associated fundamental operator.

Cite this article

Tirthankar Bhattacharyya, Haripada Sau, -Unitaries, Dilation and a Natural Example. Publ. Res. Inst. Math. Sci. 53 (2017), no. 2, pp. 261–285

DOI 10.4171/PRIMS/53-2-2