Classifying approximable algebras

Approximable algebras were defined by Chen in his proof of the Fujita theorem in the arithmetic context. These were shown to not be necessarily subalgebras of section rings of big line bundles in a previous prepreint of the author. Here, we show that whilst approximable algebras are not necessarily subalgebras of section rings of big line bundles, they are necessarily subalgebras of section rings of infinite sums of Weil divisors.