バナッハ環
The prototypical example of a Banach algebra is formula_6, the space of (complex-valued) continuous functions on a locally compact (Hausdorff) space that vanish at infinity. formula_6 is unital if and only if "X" is compact. The complex conjugation being an involution, formula_6 is in fact a C*-algebra. More generally, every C*-algebra is a Banach algebra.