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Uncomplemented uniform algebras
Authors:S V Kislyakov
Institution:1. Leningrad State University, USSR
Abstract:Let A be a closed subalgebra of the algebra of all complex-valued continuous functions on a compact space X, and suppose A contains the constant functions and separates points of X; let I be a closed ideal of A such that for some linear multiplicative functional ? on A we have the relation 0 > ∥?∣r∥ > 1 (for the existence of such an ideal it is sufficient that in the maximal ideal space of the algebra A there exists a Gleason part consisting of at least two points). Then the Banach space A** is not injective in particular, A is not a complemented subspace of C(X)].
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