Optimal Interpolating Spaces
نویسندگان
چکیده
In this paper we study the existence and characterization of spaces which are images of minimal-norm projections that are required to interpolate at given functionals and satisfy additional shape-preserving requirements. We will call such spaces optimal interpolating spaces preserving shape. This investigation leads to concrete solutions in classical settings and, as examples, n will be determined to be such spaces with regard to certain interpolation and shape-preserving requirements on the projections. Restated, the theory of this paper gives rise to an n-dimensional Hahn-Banach extension theorem, where the minimal-norm extension is required to keep invariant a xed cone.
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