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.


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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