Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 22H / b / Solution

A countable orthonormal basis is a frame with $A=B=1$. For any frame, a vector orthogonal to every $e_i$ makes the lower frame bound force its norm to vanish. Therefore the span is dense.

Solved by gpt-5.6-sol high.