We obtain a complete characterization of the norm attainment set of a bounded linear operator between normed spaces, in terms of semi-inner-product(s) defined on the space. In particular, this answers an open question raised recently in [D. Sain, On the norm attainment set of a bounded linear operator, J. Math. Anal. Appl., 457 (2018), 67–76]. Our results illustrate the applicability of semi-inner-products towards a better understanding of the geometry of normed spaces.

中文翻译：

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赋范空间中有界线性算子和半内积的范数到达集

根据空间上定义的半内积，我们获得了赋范空间之间有界线性算子的范数达到集的完整表征。特别是，这回答了最近在[D. Sain，关于有界线性算子的范数达到集，J。Math。肛门 应用 ，457（2018），67-76]。我们的结果说明了半内积对更好地理解赋范空间几何的适用性。