A simple proof of necessity in the McCullough-Quiggin theorem

TL;DR

This paper provides a straightforward proof of the necessity condition in the McCullough-Quiggin theorem, which characterizes positive semi-definite kernels with the complete Pick property.

Contribution

It introduces a simple and concise proof of the necessity part of the McCullough-Quiggin theorem, simplifying understanding of the characterization.

Findings

Proof of necessity in the McCullough-Quiggin theorem is simplified

Clarifies the conditions for positive semi-definite kernels with the complete Pick property

Enhances theoretical understanding of kernel characterization

Abstract

A short and simple proof of necessity in the McCullough-Quiggin characterization of positive semi-definite kernels with the complete Pick property is presented.