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## Main Question or Discussion Point

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?

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?