In this paper we investigate the structure of a proximinal subspace G of C(Q) of codimension n, in terms of the geometry of the range of the vector measure ν=(ν 1,...,ν n), where (ν 1,...,ν n) is a basis for the annihilator G ⊥. In particular, we prove that if ν is non-atomic, G is proximinal iff for every P∈ExtR(ν) there exists a clopen subset C of ∪ n i=1S(ν i) such that ν(C)=P.
Proximinal subspaces of C(Q) of finite codimension
CENTRONE, Francesca;
1999-01-01
Abstract
In this paper we investigate the structure of a proximinal subspace G of C(Q) of codimension n, in terms of the geometry of the range of the vector measure ν=(ν 1,...,ν n), where (ν 1,...,ν n) is a basis for the annihilator G ⊥. In particular, we prove that if ν is non-atomic, G is proximinal iff for every P∈ExtR(ν) there exists a clopen subset C of ∪ n i=1S(ν i) such that ν(C)=P.File in questo prodotto:
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