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2 results

  • 5 - Finite-Dimensional Normed Spaces

  • from Part II - Normed Linear Spaces
  • James C. Robinson, University of Warwick
  • Book:
    An Introduction to Functional Analysis
    Published online:
    21 March 2020
    Print publication:
    12 March 2020, pp 66-70

  • Summary

    We investigate finite-dimensional normed spaces. We show that in a finite-dimensional space, all norms are equivalent, and that being compact is the same as being closed and bounded. We also show that a normed space is finite-dimensional if and only if its closed unit ball is compact, using Reisz’s Lemma.

  • SHARP CONSTANTS BETWEEN EQUIVALENT NORMS IN WEIGHTED LORENTZ SPACES

  • Part of
  • SORINA BARZA, JAVIER SORIA
  • Journal:
    Journal of the Australian Mathematical Society / Volume 88 / Issue 1 / February 2010
    Published online by Cambridge University Press:
    22 January 2010, pp. 19-27
    Print publication:
    February 2010
    • Article
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  • For an increasing weight w in Bp (or equivalently in Ap), we find the best constants for the inequalities relating the standard norm in the weighted Lorentz space Λp(w) and the dual norm.