Reference for very basic books in Functional analysis

Question

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.

Answer 1

My top two recommendations would be Functional Analysis: A First Course by M.T Nair (very beginner friendly) and Introductory Functional Analysis with Applications by E. Kreyszig.

I also recommend the notes by V. S. Sunder for more of a spectral theoretic focus. You can also check out Functional Analysis by S. Kesavan.

Answer 2

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.

Answer 3

Maybe A Friendly Approach to Functional Analysis by A. Sasane?