Simultaneous Minimal Extensions on the Lines in L^p and the Cubic Case

If X denotes a (real) Banach space and V a subspace of X, we say that projection P_min : X → V is minimal if ||P_min|| ≤ ||P|| for every
projection P from X to V . We take a view on minimal projections as minimal extensions of operators and consider generalizations of the Hahn-Banach Theorem, such as the simultaneous extension of operators. As an application we consider X = [1, t, t^2 , t^3 ] (the cubic polynomials) as a subspace of Lebesgue space L^4 [−1, 1] and project X onto V = [1, t], the subspace of lines. We obtain new numerical results in this direction.