If $X$ is a Banach space, then I want to know if $X\times X$ is also Banach. What is the norm of that space?
So for example, we know $C^k(\Omega)$ is Banach and I have a vector $v = (u_1, u_2)$ where $u_i \in C^k(\Omega)$ and I want to use properties on this vector.
Thanks