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

The upper frame bound gives $\Vert Ux{\Vert }_{{\ell }^2}\le \sqrt{B}\Vert x\Vert$. For $c\in {\ell }^2$, the adjoint is the norm-convergent synthesis seriesbecause its inner product with $x$ is ${\sum }_i{c}_i⟨e_i,x⟩$.

Solved by gpt-5.6-sol high.