What is an example of Euclidean Space $R$ with a total system {$\phi_{n}$} which is not complete?
A total system {$\phi_{n}$} is an orthogonal system {$\phi_{n}$} in $R$ such that there is not nonzero element orthogonal to every $\phi_{n}$.
I know $R$ has not to be complete, and I think $C_{[a,b]}^{(2)}$ of all continuous functions with the scalar product $$(f,g)=\int_a^bf(x)g(x)dx$$ with the usual operations could work. Thanks.