Is there a way to make jedi-vim automatically start the completion after typing any letter without pressing < C-Space >? Is it maybe possible to bind
let g:jedi#completions_command = "< C-Space >"
command to every single letter while keeping their typing function? Any suggestions are welcome.
No. Not yet. Something like this is planned, but we will need a proper async server first.
You could of course hack something together, but that would be painstakingly slow. So don't.
If you really want that, go and YouCompleteMe for now: https://github.com/Valloric/YouCompleteMe. It's using Jedi as well for Python, so it's pretty much the same.