## Extensions of linear operators from hyperplanes of $$l_ \infty^{(n)}$$.(English)Zbl 0831.41014

Summary: Let $$Y\subset l_\infty^{(n)}$$ be a hyperplane and let $$A\in {\mathcal L} (Y)$$ be given. Denote $${\mathcal A}= \{L\in {\mathcal L} (l_\infty^{(n)}), Y$$: $$L|Y= A\}$$ and $$\lambda_A= \inf \{|L|$$: $$L\in {\mathcal A}\}$$. In this paper the problem of calculating of the constant $$\lambda_A$$ is studied. We present a complete characterization of those $$A\in {\mathcal L} (Y)$$ for which $$\lambda_A= |A|$$. Next we consider the case $$\lambda_A> |A|$$. Finally some computer examples will be presented.

### MSC:

 41A35 Approximation by operators (in particular, by integral operators) 41A52 Uniqueness of best approximation 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 41A55 Approximate quadratures
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