On a result of Bo\.zejko on extension of positive definite kernels

TL;DR

This paper provides a conceptual proof of Bożejko's result on extending positive definite kernels, offering a new perspective on a fundamental mathematical theorem.

Contribution

It introduces a novel conceptual proof for Bożejko's extension theorem, enhancing understanding of positive definite kernels.

Findings

A new conceptual proof of Bożejko's extension result

Clarification of the underlying principles of positive definite kernels

Potential implications for related areas in functional analysis

Abstract

A conceptual proof of the result of Bo{\.z}ejko on extension of positive definite kernels is given.