Orthonormal Basis on Hilbert Spaces

Here we collect statements about basis on Hilbert spaces . Let \(H\) denote a Hilbert space.

• For every orthonormal system \(S\subseteq H\) there exists a orthonormal basis containing \(S\) (see (0x68ef1c03) ). This is even true for inner product spaces.
• Orthonormal basis are almost a vector basis (see (0x68ef20c9) )
• Every separable Hilbert space possesses a countable orthonormal basis (see (0x68ef2135) ).