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The converse of the real positive approximate identity lemma for $L^p$ -operator algebras
Converse conjecture. The converse is always true for $L^p$ -operator algebras: if $A$ is bi-approximately unital, then $A$ has a real positive contractive approximate identity.
Conjectureopenapproximate-identities lp-operator-algebras operator-algebrasarXiv posted 2 days ago

The converse of the real positive approximate identity lemma for LpL^pLp-operator algebras