On minimal interpolating projections and trace duality

We construct a two-dimensional subspace V ⊂ C ( K ) such that an interpolating projection on V is a minimal projection with the norm >1. That answers a question posed by B. L. Chalmers. It also answers a question posed implicitly by a theorem of P. Morris and E. W. Cheney. We also give a quantitative generalization of the above mentioned theorem. As is suggested by the title, we use trace duality to obtain these results.