Mathematical Notes

, Volume 58, Issue 2, pp 785–793 | Cite as

Existence of best approximation elements inC(Q,X)

  • L. P. Vlasov
Article
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Abstract

Generalizing the result of A. L. Garkavi (the caseX = ℝ) and his own previous result concerningX = ℂ), the author characterizes the existence subspaces of finite codimension in the spaceC(Q, X) of continuous functions on a bicompact spaceQ with values in a Banach spaceX, under some assumptions concerningX. Under the same assumptions, it is proved that in the space of uniform limits of simple functions, each subspace of the form
$$\left\{ {g \in B:\smallint _Q \left\langle {g(t),d\mu _i } \right\rangle = 0,i = 1,...,n} \right\},$$
whereμi ∈ C(Q, X)* are vector measures of regular bounded variation, is an existence subspace (the integral is understood in the sense of Gavurin).

Keywords

Continuous Function Simple Function Bounded Variation Approximation Element Vector Measure 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • L. P. Vlasov
    • 1
  1. 1.Institute of Mathematics and MechanicsUrals Branch of the Russian Academy of SciencesUfa

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