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It's the same thing really. It's just that Riesz first proved it for the special case and it was then generalized to Hilbert spaces. It's such a huge generaliza
by turminal 5y ago
It's the same thing really. It's just that Riesz first proved it for the special case and it was then generalized to Hilbert spaces. It's such a huge generalization that it causes a lot of confusion.
- ogogmad 5y agoC([0,1]) is not a Hilbert space but a Banach space. Every Hilbert space is a Banach space, but not vice versa. The version of the theorem for Hilbert spaces is indeed a lot easier to prove than the one given in the article.
- turminal 5y agoAnd that just proves my point about confusion :) Thanks for the correction.