Constructive proof of the Carpenter's Theorem

TL;DR

This paper provides a constructive proof of Carpenter's Theorem, extending Kadison's original result to include the real case, offering a new approach to this mathematical theorem.

Contribution

The paper introduces a constructive proof method for Carpenter's Theorem that also covers the real case, which was not addressed in the original proof.

Findings

Constructive proof of Carpenter's Theorem

Extension to the real case of the theorem

New approach differs from original proof

Abstract

We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.