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I am a new student in the field of functional analysis. I'm looking for references that make sense for all kinds of vector spaces, such as the difference between $L^2$ and $l^2$ and others like: $C_0$ ,$C^1$, etc...

Thanks.

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The keywords would be: normed vector spaces, Banach spaces, Hilbert spaces...rather than vector spaces. For instance, $L^2(0,1)$ and $\ell^2$ are isomorphic as vector spaces. –  1015 Mar 4 '13 at 19:06
    
How experienced are you in analysis? The thing is, functional analysis is typically not the study of specific linear spaces, but rather of more general properties of large classes of linear spaces (in particular, locally convex spaces, Banach spaces, Hilbert spaces). I guess I just mean to say that you might not find what you're looking for in a book just about functional analysis. –  Christopher A. Wong Mar 5 '13 at 0:40
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If you are looking for a book and are not afraid of thick, old books, try to get your hands on a copy of "Linear Operators I" by Dunford and Schwarz (from 1958, I think). It's dense but contains a lot of cool and unique stuff.

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