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I need a book or lecture notes for the course functional analysis, which I took this semester, the lecturer mentioned some book at the beginning and currently I'm also reading the book of Vitali Milman but some chapters, we treated in the lecture, are not contained in the book (the starred chapters below), and during my last semesters I made the experience, that it is not good to use ten different sources for a course, so I'm asking for a more complete book, some subjects we covered till now are:

Normed vector spaces

Banach spaces

Hilbert Spaces

Orthogonality

Projection theorem

Separable Spaces

Bessel's inequality, Parseval's formula

Stone-Weierstrass*

Hamel Basis*

Linear funtionals-Hyperplanes*

Summable Series in Banach spaces*

Dini's theorem*

Riemann-Lebesgue lemma*

Dirichlet kernel, Féjer kernel*

Banach-Steinhaus

Baire's Theorem

Open mapping theorem

Closed Graph theorem

Hahn-Banach

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The books which a student should follow are the ones listed in order:

1.Introductory Functional Analysis with Applications:Erwin Kreyszig

2.Functional Analysis: Bachman ,Narici.

3.Elias M.Stein,Rami Shakarchi:Functional Analysis

4.Angus E.Taylor,David Lay:Introduction to Functional Analysis

5.Introduction to Functional Analysis: J.B.Conway

The first one is a friendly introduction ,the second one is a more complete book with lots of worked out examples.

The third one is a beautiful text to accompany the first two.

You can try out $4,5$ if you want.The above $3$ would suffice.

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  • $\begingroup$ the first and the second are excellent thanks $\endgroup$ – ketum Nov 14 '15 at 13:48
  • $\begingroup$ You are welcome @ketum $\endgroup$ – Learnmore Nov 14 '15 at 13:54

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