Codimension-one minimal extensions onto Haar subspaces

Let H"n be an n-dimensional Haar subspace of C"R[a,b] and H"n"-"1 be an n-1-dimensional Haar subspace of H"n. Let A be a linear, continuous operator on H"n"-"1. In this note we show that if a norm of minimal extension of A from H"n into H"n"-"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.

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