Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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RESEARCH ON NORMAL STRUCTURE IN A BANACH SPACE VIA SOME PARAMETERS IN ITS DUAL SPACE

  • Gao, Ji (Department of Mathematics Community College of Philadelphia)
  • Received : 2018.03.18
  • Accepted : 2018.11.07
  • Published : 2019.04.30
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Abstract

Let X be a Banach space and $X^*$ be its dual. In this paper, we give relationships among some parameters in $X^*$: ${\varepsilon}$-nonsquareness parameter, $J({\varepsilon},X^*)$; ${\varepsilon}$-boundary parameter, $Q({\varepsilon},X^*)$; the modulus of smoothness, ${\rho}_{X^*}({\varepsilon})$; and ${\varepsilon}$-Pythagorean parameter, $E({\varepsilon},X^*)$, and weak orthogonality parameter, ${\omega}(X)$ in X that imply uniform norm structure in X. Some existing results are extended or approved.

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References

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