# A proof of Boca's Theorem

## TL;DR

This paper introduces a general method for extending unital completely positive maps to amalgamated free products of C*-algebras and provides a dilation theoretic proof of Boca's Theorem.

## Contribution

It presents a novel approach to extending maps and offers a new proof of Boca's Theorem using dilation theory.

## Key findings

- Extension method for unital completely positive maps
- Dilation theoretic proof of Boca's Theorem
- Applicable to amalgamated free products of C*-algebras

## Abstract

We give a general method of extending unital completely positive maps to amalgamated free products of C*-algebras. As an application we give a dilation theoretic proof of Boca's Theorem.