Proximinal Subspaces of C(Q) of Finite Codimension
نویسندگان
چکیده
منابع مشابه
Proximinal and Strongly Proximinal Subspaces of Finite codimension
Let X be a normed linear space. We will consider only normed linear spaces over R (Real line), though many of the results we describe hold good for n.l. spaces over C (the complex plane). The dual of X, the class of all bounded, linear functionals on X, is denoted by X∗. The closed unit ball of X is denoted by BX and the unit sphere, by SX . That is, BX = {x ∈ X : ‖x‖ ≤ 1} and SX = {x ∈ X : ‖x‖...
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We study an analogue of Garkavi’s result on proximinal subspaces of C(X) of finite codimension in the context of the space A(K) of affine continuous functions on a compact convex set K. We give an example to show that a simple-minded analogue of Garkavi’s result fails for these spaces. When K is a metrizable Choquet simplex, we give a necessary and sufficient condition for a boundary measure to...
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It follows from [1] and [7] that any closed n-codimensional subspace (n ≥ 1 integer) of a real Banach space X is the kernel of a projection X → X, of norm less than f(n) + ε (ε > 0 arbitrary), where f(n) = 2 + (n − 1) √ n + 2 n + 1 . We have f(n) < √ n for n > 1, and f(n) = √ n − 1 √ n + O (
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1999
ISSN: 0021-9045
DOI: 10.1006/jath.1999.3361