Stinespring dilation theorem

In mathematics, Stinespring's dilation theorem, also called Stinespring's factorization theorem, named after W. Forrest Stinespring, is a result from operator theory that represents any completely positive map on a C*-algebra A as a composition of two completely positive maps each of which has a special form: A *-representation of A on some auxiliary Hilbert space K followed by An operator map of the form T ↦ V*TV. Moreover, Stinespring's theorem is a structure theorem from a C*-algebra into the algebra of bounded operators on a Hilbert space. Completely positive maps are shown to be simple modifications of *-representations, or sometimes called *-homomorphisms.

Source: Wikipedia — Stinespring dilation theorem (CC BY-SA 4.0)

Stinespring dilation theorem

In mathematics, Stinespring's dilation theorem, also called Stinespring's factorization theorem, named after W. Forrest Stinespring, is a result from operator theory that represents any completely positive map on a C*-algebra A as a composition of two completely positive maps each of which has a special form: A *-representation of A on some auxiliary Hilbert space K followed by An operator map of the form T ↦ V*TV. Moreover, Stinespring's theorem is a structure theorem from a C*-algebra into the algebra of bounded operators on a Hilbert space. Completely positive maps are shown to be simple modifications of *-representations, or sometimes called *-homomorphisms.

This neuron ends here.

Source: Wikipedia "Stinespring dilation theorem" · CC BY-SA 4.0

Share this article: X · Bluesky
Privacy Policy