3 problems

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The codimension trichotomy conjecture for commutator spaces of operator ideals
Codimension trichotomy conjecture. If $I\ne F+[I,B(H)]$ , then
Conjectureopencodimension commutator-spaces operator-idealsarXiv posted 2 days ago
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The one-or-infinity codimension conjecture for commutator spaces
One-or-infinity codimension conjecture. For small ideals, the codimension of $[I,B(H)]$ in $I$ can be only one or infinity; for large ideals, it can be only zero or infinity.
Conjectureopencommutator-spaces functional-analysis operator-idealsarXiv posted 2 days ago
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The none-one-infinity conjecture for traces on operator ideals
None-one-infinity conjecture. The number of traces that an ideal can support must always be either none, one, or infinitely many.
Conjectureopencommutator-spaces operator-ideals tracesarXiv posted 2 days ago

The codimension trichotomy conjecture for commutator spaces of operator ideals