Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지

A METRIC ON NORMED ALMOST LINEAR SPACES

  • Published : 1999.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce a semi-metric on a normed almost linear space X via functional. And we prove that a normed almost linear space X is complete if and only if $V_X$ and $W_X$ are complete when X splits as X=$W_X$ + $V_X$. Also, we prove that the dual space $X^\ast$ of a normed almost linear space X is complete.

Keywords

References

  1. Suppl. Rend. Circ. Mat. Palermo II. Ser. v.5 An approach to generalizing Banach spaces: Normed almost linear spaces, Proceedings of the 12th Winter School on Abstract Analysis (Srni 1984) G. Godini
  2. J. Approx. Theory v.43 A framework for best simultaneous approximation: Normed almost linear spaces G. Godini
  3. Math. Ann. v.279 On normed almost linear spaces G. Godini
  4. Comm. Korean Math. Soc. v.12 A characterization of reflexivity of normed almost linear spaces S. M. Im;S. H. Lee
  5. Bull. Korean Math. Soc. v.34 A metric induced by a norm on normed almost linear spaces S. M. Im;S. H. Lee