Induced Stinespring factorization and the Wittstock support theorem

J. E. Pascoe; Ryan Tully-Doyle

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arXiv · 2204.02963

Induced Stinespring factorization and the Wittstock support theorem

J. E. Pascoe·Ryan Tully-Doyle

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Abstract

Given a pair of self-adjoint-preserving completely bounded maps on the same $C^*$-algebra, say that $\varphi \leq \psi$ if the kernel of $\varphi$ is a subset of the kernel of $\psi$ and $\psi \circ \varphi^{-1}$ is completely positive. The \emph{Agler class} of a map $\varphi$ is the class of $\psi \geq \varphi.$ Such maps admit colligation formulae, and, in Lyapunov type situations, transfer function type realizations on the Stinespring coefficients of their Wittstock decompositions. As an application, we prove that the support of an extremal Wittstock decomposition is unique.

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BibTeX RIS

J. E. Pascoe, Ryan Tully-Doyle. 2022-04-06. Induced Stinespring factorization and the Wittstock support theorem. https://arxiv.org/abs/2204.02963

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