Strongly proximinal subspaces of finite codimension in C(K)
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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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2007
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm109-1-10