The determination of minimal projections and extensions in

Authors:
B. L. Chalmers and F. T. Metcalf

Journal:
Trans. Amer. Math. Soc. **329** (1992), 289-305

MSC:
Primary 41A35; Secondary 41A65

DOI:
https://doi.org/10.1090/S0002-9947-1992-1034660-1

MathSciNet review:
1034660

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Abstract: Equations are derived which are shown to be necessary and sufficient for finite rank projections in to be minimal. More generally, these equations are also necessary and sufficient to determine operators of minimal norm which extend a fixed linear action on a given finite-dimensional subspace of and thus may be viewed as an extension of the Hahn-Banach theorem to higher dimensions in the setting. These equations are solved in terms of an best approximation problem and the required orthogonality conditions. Moreover, this solution has a simple geometric interpretation. Questions of uniqueness are considered and a number of examples are given to illustrate the usefulness of these equations in determining minimal projections and extensions, including the minimal projection onto the quadratics.

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1034660-1

Article copyright:
© Copyright 1992
American Mathematical Society