A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
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Dual space of Bochner space
Let $B$ be a refexive Banach space. I want to show that
$$(L^2(0,T;B))^* = L^2(0,T;B^*)$$ and that
the dual pairing is
$$\langle F,f \rangle_{L^2(0,T;B^*), L^2(0,T;B)} = \int_0^T \langle F(t), f(t) ...
