Re: separable Hilbert space


michaeld wrote:
> David Macmanus wrote:
> > Can anyone give an example of a Hilbert space that isn't separable?
> > Separable Hilbert spaces have orthonormal bases which are either finite
> > or infinite, but countable. So I guess I'm wondering what's a space that
> > has an uncountable basis set of vectors.
> > Thanks,
> > David.
>
> Let I be some big index set. Let H be the set of all complex valued
> sequences v indexed by I, i.e. v: I->C, such that:
>
> sum |v(i)|^2
> I
>
> is finite. Note that if the sequence v is in H then this condition
> implies that all but countably many of the v(i) must equal zero.

Why? Did you mean to say that v(i) is limited in value to 0,1?

.

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