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Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.

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If either $A$ is exact or $B$ is nuclear then every closed ideal of $A\otimes_{min}B$ is of ...

When A is simple, it's proved in: https://doi.org/10.1002/mana.201700009 As per the suggestion (below) by leo monsaingeon, here are the details reproduced from above paper: Statement: Let $A$ and $B$ …
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