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A Phelps type result for spaces with asymmetric norms

Abstract


If \((X,||\cdot|)\) is a linear space with asymmetric norm and \(Y\) is a \(X\), for every \(f\in Y_{+}^{\ast}\) (the cone of linear bounded functional on \(Y\)) there exists functional \(F\in Y_{+}^{\ast}\) extending \(f\) and preserving the asymmetric norm of \(f\).The problem of uniqueness of the extension in terms of uniqueness of elements of best of \(F\in X_{+}^{\ast}\) by elements of \(Y_{+}^{\perp}=\{G\in X_{+}^{\ast}:\left. G\right \vert _{Y}-0,F\geq G\}\), is discussed.

Authors

Costica Mustăţa
“Tiberiu Popoviciu”  Institute of Numerical Analysis, Romanian Academy,  Romania

Keywords

asymmetric norm; extension and approximation.

Paper coordinates

C. Mustăţa, A Phelps type result for spaces with asymmetric norms, Bul. Şt. Univ. Baia Mare, Seria B, Fascicola matematică-informatică, 18 (2002) no. 2, 275-280.

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Journal

Bul. St. Univ. Baia Mare

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2002

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