3 problems

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A separable intermediate-space conjecture for M-approximate identities
Let $X$ be the Banach space from Proposition 3.16, which is an $M$ -ideal in $X^{**}$ but admits no $M$ -approximate identity in $X^{**}$ . Separable intermediate-space conjecture. Th…
Conjectureopenapproximate-identities banach-spaces operator-spacesarXiv posted 2 days ago
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Collins–Fontenot conjecture on approximate identities in $C_0(X)$
Collins–Fontenot conjecture. The following conditions are equivalent: $X$ is paracompact; $C_0(X)$ has a strictly totally bounded canonical approximate identity; and $C_0(X)$ has a…
Conjectureopenapproximate-identities functional-analysis topological-algebrasarXiv posted 2 days ago
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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

A separable intermediate-space conjecture for M-approximate identities