Hi all,

First, I have a trivial question on the definition of the {u_n}(finite orthonormal system) that's mentioned at the introduction of this section in lecture note #14.

Is this set/system defined in H, in which you did not mention whether it's infinite or finite? or does it span its own space(any) based on perhaps infinite/finite number of linear hulls including K, which in particular belongs to H?

Also In the following Theorem 1

b) I think this implies w is linear independent of other elements in K, regardless of "unique" in a) or c)

c) do you mean "w in K"(summation of alpha times u_n) rather than equal to it?

Thanks in advance.