# closed lattice ideal is isomorphic to $C(K)$

Let $$X\in E$$, where $$E$$ is a Banach function space on $$(0,1)$$. Consider the interval $$[-X,X]$$ and generate it to a closed lattice ideal $$I$$ of $$E$$. We may renorm this ideal $$I$$ such that $$[-X,X]$$ is the unit ball. Why is $$I$$ lattice-isomorphic to $$C(K)$$? Here, $$K$$ is a compact space.