A Phelps type result for spaces with asymmetric norms

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.

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

asymmetric norm; extension and approximation.

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.

https://www.jstor.org/stable/44001869

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