Abstract
This chapter deals with the highly successful theory of dilation on the symmetrized bidisc. This involves the joint spectrum which we begin with. We then describe the concept of a spectral set. This leads us to the symmetrized bidisc. Its properties are studied. In preparation for dilation, we study an operator valued version of the Fejer-Riesz theorem. Then a pair of operators for which the symmetrized bidisc is a spectral set is considered and its dilation is explicitly constructed. A large class of examples is given.
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Bhat, B.R., Bhattacharyya, T. (2023). Dilation Theory in Several Variables—The Symmetrized Bidisc. In: Dilations, Completely Positive Maps and Geometry. Texts and Readings in Mathematics, vol 84. Springer, Singapore. https://doi.org/10.1007/978-981-99-8352-0_6
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