A remark on embedding of a cylinder on a real commutative Banach algebra

Let A be a real commutative Banach algebra with unity. Let a_0\in A\setminus\{0\}. Let \mathbb Z a_0:=\{na_0\}_{n\in \mathbb Z}. Then, \mathbb Z a_0 is a discrete subgroup of A. For any n\in \mathbb Z, the Frechet derivative of the mapping x \, \in \, A \ \ \ \mapsto \... Show more