Mathematical Notes

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

Existence of best approximation elements inC(Q,X)

  • L. P. Vlasov


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).


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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