# What is the dual space of $C([0,T];X)$ ($X$ Hilbert space)?

What is the dual space of $C([0,T];X)$, where $X$ is a Hilbert space? Is it $\operatorname{BV}([0,T]; X^*)$?

As we know, for $C([0,T])$, the dual space is $\operatorname{BV}([0,T])$, but when it is continuous with vector values in $X$, is it still true?

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Duplicate of Riesz representation and vector-valued functions –  user53153 Dec 27 '12 at 8:16