Let \(H\) be a Hilbert space. A family \((u_{n})_{n\geq 1}\) of vectors in \(H\) is complete if the only \(x\in H\) with \(\inner{x}{u_{n}} = 0\) for all \(n\) is \(x = 0\).
Complete families in a Hilbert space
D-SLYE5
D-SLYE5
Let \(H\) be a Hilbert space. A family \((u_{n})_{n\geq 1}\) of vectors in \(H\) is complete if the only \(x\in H\) with \(\inner{x}{u_{n}} = 0\) for all \(n\) is \(x = 0\).