대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제34권1호
  • /
  • Pages.115-125
  • /
  • 1997
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

A metric induced by a norm on normed almost linear spaces

  • Im, Sung-Mo (Department of Mathematics, College of Natural Science, Chungbuk National University, Cheongju 360-763) ;
  • Lee, Sang-Han (Department of Mathematics, College of Natural Science, Chungbuk National University, Cheongju 360-763)
  • 발행 : 1997.02.01
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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

참고문헌

  1. Normed linear spaces M. M. Day
  2. Pure and applied Mathematics v.7 Linear operators. N. Dunford;J. Schwartz
  3. Proceedings of the 12th Winter School on Abstract Analysis (Srni 1984) Suppl. Rend. Circ. Mat. Palermo Ⅱ. Ser. v.5 An approach to generalizing Banach spaces : Normed almost linear spaces G. Godini
  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