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I have recently finished reading the first half of the book Real Analysis by N.L.Carothers, which includes upto compactness and baire category theorems. In this half the author has introduced norms and some analysis on the norm vector spaces. But I am not at all comfortable with norms and for this I have skipped most of the problems on norms, $l_{p}$ spaces, hilbert cube, space of continuous functions etc. But before starting the second half of the book titled 'Function Spaces' I want to become more famliar with these concepts. I want to know if there is any book with this concepts described more deeply or some book having more problems on norms and $l_{p}$ spaces.

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  • $\begingroup$ Try Kreyszig "Introduction to Functional Analysis with Applications. " $\endgroup$ – Lisa Jul 31 '17 at 19:44

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