Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Extreme Points, Exposed Points and Smooth Points of the Space 𝓛s(2𝑙3∞)

  • Kim, Sung Guen (Department of Mathematics, Kyungpook National University)
  • Received : 2019.09.05
  • Accepted : 2020.04.21
  • Published : 2020.09.30
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Abstract

We present a complete description of all the extreme points of the unit ball of 𝓛s(2𝑙3∞) which leads to a complete formula for ║f║ for every f ∈ 𝓛s(2𝑙3∞)∗. We also show that $extB_{{\mathcal{L}}_s(^2l^3_{\infty})}{\subset}extB_{{\mathcal{L}}_s(^2l^n_{\infty})}$ for every n ≥ 4. Using the formula for ║f║ for every f ∈ 𝓛s(2𝑙3∞)∗, we show that every extreme point of the unit ball of 𝓛s(2𝑙3∞) is exposed. We also characterize all the smooth points of the unit ball of 𝓛s(2𝑙3∞).

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References

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