Reference for very basic books in Functional analysis

book-recommendationfunctional-analysis

I'm confused about which books I have to read for Functional analysis for the beginner level.

I need references for very basic books in Functional analysis and that book must contain given Topics below

$1.$ Normed linear spaces,

$2.$ Banach spaces,

$3.$ Hilbert spaces,

$4.$ Compact operators.

$5.$ Properties of $ C[0;1]$ and $L^p[0;1]$

$6.$ Continuous linear maps (linear operators).

$7.$ Hahn-Banach Theorem, Open mapping theorem,

$8.$ Closed graph theorem and the uniform boundedness principle.

Best Answer

As @Jan mentioned in the comments, Kreyszig's text on functional analysis is a great introduction and has all the topics that you're looking for. It also has a great deal of applications which other texts seem to ignore. However, it does not cover the measure theoretic aspects of the theory.

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