Hilbert Space Orthonormal Sets: Alternative to Rudin

[Hjensen]

I am taking a course on Hilbert spaces and we're using Walter Rudins "Real and complex analysis", which I am generally very happy about.

However, I don't think the section about orthonormal sets (page 82-87) is that nice. In particular, I would like to see a different approach to the theorem 4.18. Does anyone have a suggestion to another text on orthonormal sets/orthonormal bases in a Hilbert space?

 

[micromass]

I would suggest "Introductory Functional Analysis" by Kreyszig. The theorem you want is on page 170.

 

[mathwonk]

a book liked as a student was by edgar lorch, spectral theory. this theorem is on page 68, thm. 3-5, but the proof builds up over several previous pages.

Another good book is Foundations of moden analysis, by Dieudonne, where this material is treated in chapter VI.5.

Anything by George Simmons is also recommended as especially clear.

or introduction to hilbert space by sterling k. berberian. I recall as an undergradutae that I could follow easily every argument in berberian.

Indeed this stuff is available in many places. You might even just try to prove the results yourself, and see how far you get. then read a book to fill in the rest.

In most cases Rudin is my absolute last place to look for something understandably explained. He is one of the few remaining authors (except me sometimes) who seems to take especial pride in being as brief as possiBle instead of being clear.

 

[Hjensen]

Thanks a lot guys. I'll look into that.