Codimension-one minimal extensions onto Haar subspaces

Let HnHn be an nn-dimensional Haar subspace of CR[a,b]CR[a,b] and Hn−1Hn−1 be an n−1n−1-dimensional Haar subspace of HnHn. Let AA be a linear, continuous operator on Hn−1Hn−1. In this note we show that if a norm of minimal extension of AA from HnHn into Hn−1Hn−1 is greater than the operator norm of AA, then it is a strongly unique minimal extension. Moreover, we prove, with a slightly stronger assumptions, that minimal extension of AA is a generalized (see Definition 8) interpolating operator.