Codimension-one minimal extensions onto Haar subspaces

Abstract

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