An element "lives" in a space
I have seen the expression, "X is the Hilbert space in which the element x lives". As a native speaker, this seems quite sloppy to me. Is there a more succinct way to formulate this expression?
Solution 1:
You could say:
X is in the Hilbert space to which the element x belongs.
Though I don't think using "lives" is necessarily wrong (it is a bit informal, though).