Commutators on Banach spaces over non-Archimedean fields

We prove, among other things, that every operator on an infinite-dimensional Banach space E over a non-Archimedean field K is a commutator, if the valuation of K is discrete (in particular, if K is locally compact) or if E has an orthogonal basis (in particular, if E is of countable type).

Automated summary

We prove that in an infinite-dimensional Banach space E over a non-Archimedean field K, every operator is a commutator if the valuation of K is discrete (especially if K is locally compact) or if E has an orthogonal basis (especially if E is of countable type).