Hi sorry if it seems evident but i need a help for these statements
1)$N(u)=\sup_{t\in R^{+}}\|u(t)\|_{L^{2}(\omega)}$it is not a norm?and if it is not which norm i need to choose for space $C((0,\infty,L^{2}(\omega))$? i think that i cant found such norm because $(0,\infty)$ is not compact
- if i want to prove that a function $u\in C((0,\infty,L^{2}(\omega))$ i need to prove that $u \in C((0,T,L^{2}(\omega))$ for all $T>0$ is this statement true?
$\omega$ is bounded open set $\subset R^{n}$ thanks