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- W4224944806 abstract "A commuting triple of Hilbert space operators $(A,B,P)$, for which the closed tetrablock $bar{mathbb E}$ is a spectral set, is called a textit{tetrablock-contraction} or simply an $mathbb E$-textit{contraction}, where [ mathbb E={(a_{11},a_{22}, det A):, A=[a_{ij}]in mathcal M_2(mathbb C), ; |A| <1 } subset mathbb C^3 ] is a polynomially convex domain which is naturally associated with the $mu$-synthesis problem. We introduce triangular $mathbb E$-contractions and prove that every pure triangular $mathbb E$-contraction dilates to a pure triangular $mathbb E$-isometry. We construct a functional model for a pure triangular $mathbb E$-isometry and apply that model to find a new proof for the famous Berger-Coburn-Lebow Model Theorem for commuting isometries. Next we give an alternative proof to the more generalized version of Berger-Coburn-Lebow Model, namely the factorization of a pure contraction due to Das, Sarkar and Sarkar (textit{Adv. Math.} 322 (2017), 186 -- 200). We find a necessary and sufficient condition for the existence of $mathbb E$-unitary dilation of an $mathbb E$-contraction $(A,B,P)$ on the smallest dilation space and show that it is equivalent to the existence of a distinguished variety in $mathbb E$ when the defect space $D_{P^*}$ is finite dimensional." @default.
- W4224944806 created "2022-04-28" @default.
- W4224944806 creator A5080755369 @default.
- W4224944806 date "2022-04-24" @default.
- W4224944806 modified "2023-09-24" @default.
- W4224944806 title "Triangular Tetrablock-contractions, factorization of contractions, dilation and subvarieties" @default.
- W4224944806 doi "https://doi.org/10.48550/arxiv.2204.11387" @default.
- W4224944806 hasPublicationYear "2022" @default.
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