I have the following definition. A continuous linear operator $P:C^\infty(\mathbb T^n)\longrightarrow C^\infty(\mathbb T^n)$ is globally solvable if $P$ has closed range.
Of course I could replace $C^\infty(\mathbb T^n)$ for any topological vector space and the above definition would still make sense.
Are there papers or books dealing with such kind of concept (maybe in the context of Fréchet spaces)?
Thanks