There are many representation theorems which state that the dual space of a Banach space $X$ has a particularly concrete form. For example, if $X = C([0,1],\mathbb R)$ is the space of real-valued continuous functions on $[0,1]$, then $X^\*$ is the space of Radon measures on $[0,1]$. When you are confronted with some Banach space, where do you go to figure out a representation of its dual space? Is there a book or survey article with a rich set of examples?


Here is the particular example which motivates this question. Let $\operatorname{Sym}$ be the space of symmetric $n \times n$ real matrices with a usual matrix norm. Let $U \subseteq \mathbb R^n$ be compact, and let $X = C^{2+\alpha}(U, \operatorname{Sym})$ with the obvious norm. What is the dual space of $X$?



Examples of Banach spaces and their duals
In wikipedia, there is a [list of banach spaces](http://en.wikipedia.org/wiki/List_of_Banach_spaces) with its dual space and it also tells you if it is reflexive, for example.


