Paschke Dilations

TL;DR

This paper demonstrates that Paschke's factorization for normal maps between von Neumann algebras has a universal property and aligns with Stinespring's dilation, providing a unified understanding of these dilations.

Contribution

It establishes the universal property of Paschke's dilation for normal maps and shows its equivalence to Stinespring's dilation in von Neumann algebras.

Findings

Paschke dilation has a universal property for normal maps.

Paschke dilation coincides with Stinespring's dilation.

Provides a unified framework for dilations of normal maps.

Abstract

In 1973 Paschke defined a factorization for completely positive maps between C*-algebras. In this paper we show that for normal maps between von Neumann algebras, this factorization has a universal property, and coincides with Stinespring's dilation for normal maps into B(H).