A metric induced by a norm on normed almost linear spaces

초록

In [3,4,5], G. Godini introduced a normed almost linear space(nals), generalizing the concept of a normed linear space. In contrast with the case of a normed linear space, tha norm of a nals $(X, $\mid$$\mid$$\mid$ \cdot $\mid$$\mid$$\mid$)$ does not generate a metric on X $(for x \in X \backslash V_X we have $\mid$$\mid$$\mid$ x - x $\mid$$\mid$$\mid$ \neq 0)$.

키워드

• Almost linear space;
• Normed almost linear space;

파일

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참고문헌

1. Normed linear spaces M. M. Day
2. Pure and applied Mathematics v.7 Linear operators. N. Dunford;J. Schwartz
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4. J. Approx. Theory v.43 A framework for best simultaneous approximation: Normed almost linear spaces G. Godini
5. Math. Ann. v.279 On Normed Almost Linear Spaces G. Godini
6. Comm. Korean Math. Soc. v.10 Reflexivity of normed almost linear spaces S. H. Lee
7. Proc. Amer. Math. Soc. v.3 An embedding theorem for spaces of convex sets H. Radstrom