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Finite Dimensional Cebysev Subspaces of C*-Algebras
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In this note, a proposition due to G. K. Pedersen that characterizes a two dimensional Cebysev subspace of a C*-algebra is generalized to arbitrary finite dimension by introducing the concept of non-commutative Haar condition. In addition, the spectral condition in the two dimensional case is linked to boundary representations and Choquet boundary. Examples are provided to illustrate a comparison with classical results for function spaces.
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