A short proof of the existence of the injective envelope of an operator space

TL;DR

This paper provides a simplified proof of the existence of the injective envelope for operator spaces using Ellis' lemma, streamlining prior complex proofs.

Contribution

It introduces a new, simpler proof method for the existence of the injective envelope of operator spaces, originally established by Hamana and Ruan.

Findings

Simplified proof of injective envelope existence

Application of Ellis' lemma to operator spaces

Streamlined approach compared to previous proofs

Abstract

We use Ellis' lemma to give a simple proof of the existence of the injective envelope of an operator space first shown by work of Hamana and Ruan.