# Jordan decomposition for infinite-dimensional vector spaces: references?

Let $$V$$ be a finite-dimensional vector space over a perfect field (e.g., a characteristic zero field). The (additive) Jordan decomposition of an endomorphism $$g \in \mathrm{End}(V)$$ says that you can write $$g$$ as

$$g = g_s + g_n \ ,$$

where $$g_s$$ is semisimple and $$g_n$$ is nilpotent. The Encyclopedia of Mathematics adds that this decomposition can be generalized to locally finite endomorphisms of infinite-dimensional vector spaces.

This generalization seems quite elementary and straightforward, but I don't know any other reference where this result is developed. So I would be grateful if anyone can provide some.