Any Functional Analysis Text That Covers The Same Material As Kreyszig But In A More Rigorous Fashion? Any Notes Of A Course Taught Using Kreyszig?

Question

I've for some time been learning elementary functional analysis from the book Introductory Functional Analysis With Applications by Erwine Kreyszig.

Although Kreyszig's presentation is mostly accessible for a person with not-a-very-strong background in analysis, there often are occasions where, as I feel, he sacrifices rigor and detail in the interest of simplicity of the presentation. And, sometimes he is too verbose; sometimes he is perhaps not explicit enough. Besides, Kreyszig's text, as far as I know, is not being followed at those "elite" places like the MIT who offer such anciliary support as the MIT OCW.

So I would like to have another text that covers the same (or roughly the same) material as does Kreyszig (and preferably a text that covers this material in a more rigorous and explicit manner).

Can the esteemed Math SE community suggest any such text?

Is there any place on the Internet where I can access notes of courses taught using Kreyszig's text, especially the first four chapters?

For those who haven't got a copy of Kreyszig, here is the link to a page where it can be accessed (and perhaps can also be downloaded) for free.

http://www-personal.acfr.usyd.edu.au/spns/cdm/resources/Kreyszig%20-%20Introductory%20Functional%20Analysis%20with%20Applications.pdf

Answer 1

The following are standard (often classical) references in functional analysis that cover the area at a more advanced level than Kreyszig:

1. Rudin
2. Yosida
3. Dunford & Schwartz
4. Reed & Simon
5. Lax
6. Conway
7. Schechter