# Reference for very basic books in Functional 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.

• Kreyszig: Introductory Functional Analysis with Applications. – Jan Jun 1 '20 at 7:54
• 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. – Lorenzo Quarisa Jun 1 '20 at 9:15