Transition Probabilities of Positive Linear Functionals on $*$-Algebras

Konrad Schmüdgen

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arXiv · 1304.6322

Transition Probabilities of Positive Linear Functionals on $*$-Algebras

Konrad Schmüdgen

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Abstract

Using unbounded Hilbert space representations basic results on the transition probability of positive linear functionals $f$ and $g$ on a unital *-algebra are obtained. The main assumption is the essential self-adjointness of GNS representations $\pi_f$ and $\pi_g$. Applications to functionals given by density matrices and by integrals and to vector functionals on the Weyl algebra are given.

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BibTeX RIS

Konrad Schmüdgen. 2013-04-23. Transition Probabilities of Positive Linear Functionals on $*$-Algebras. https://arxiv.org/abs/1304.6322

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