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

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Key Points

The proof establishes the wide occurrence of injective envelopes in operator spaces, enhancing theoretical understanding.
Ellis' lemma is effectively utilized to provide a straightforward proof, demonstrating its practical application in operator space theory.
This result is built upon foundational contributions by Hamana and Ruan, affirming the continuity of research in this mathematical field.
Broad implications suggest that further studies could expand on the injective properties within operator spaces, influencing various mathematical frameworks.

This proof confirms the existence of the injective envelope of an operator space, highlighting Ellis’ lemma and prior work by Hamana and Ruan.

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.

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Thomas Sinclair (2025) studied this question.

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