On a Question of Davidson and Paulsen

We answer a question from K. R. Davidson and V. I. Paulsen (1997, J. Reine Angew Math. 487, 153–170) about the similarity to a contraction of a class of CAR-valued Foguel–Hankel operator. The proof is then used to show that for any r>0, the Schur multiplier j+1i+j+1ri,j⩾0 is bounded when restricted to Hankel matrices.