0
$\begingroup$

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.

$\endgroup$
2
  • 6
    $\begingroup$ Kreyszig: Introductory Functional Analysis with Applications. $\endgroup$ – Jan Jun 1 '20 at 7:54
  • 1
    $\begingroup$ Pretty much any introductory functional analysis textbook will cover these topics. Personally one I really like (and where I first learnt functional analysis myself) is Bhatia's 'Notes on functional analysis'. It is written in the format of lectures so it feels like following a university course. $\endgroup$ – Lorenzo Quarisa Jun 1 '20 at 9:15
1
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

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.

$\endgroup$
0
$\begingroup$

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

$\endgroup$
1
  • $\begingroup$ Welcome to Math SE. Could you edit your post to include the main idea provided by the article? Link only answer are viewed as a bad answer since link could be lost. $\endgroup$ – Alain Remillard Feb 18 at 18:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.