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Exposed 2-Homogeneous Polynomials on the two-Dimensional Real Predual of Lorentz Sequence Space

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Abstract

We classify the exposed polynomials of the unit ball of the space of 2-homogeneous polynomials on the two-dimensional real predual of Lorentz sequence space. In fact, we prove that

$$\left.\begin{array}{ll}{\rm exp}B_{{\mathcal P}(^2d_{*}(1, w)^2)} = {\rm ext}B_{{\mathcal{P}}(^2d_{*}(1,w)^2)}{\!\Big\backslash\!} \left\{\pm\left[\frac{x^2-y^2\pm 2{w}xy}{1+{w}^2}\right],\right.\\ \qquad \qquad \quad \quad \pm \left.\left[\frac{1-w}{(1+w)(1+w^2)}(x^2-y^2)\pm\frac{2}{(1+w)^2}xy\right]\right\}.\end{array}\right.$$

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Authors and Affiliations

  1. Department of Mathematics, Kyungpook National University, Daegu, 702-701, South Korea

    Sung Guen Kim

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  1. Sung Guen Kim
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Correspondence to Sung Guen Kim.

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This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2013R1A1A2057788).

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Kim, S.G. Exposed 2-Homogeneous Polynomials on the two-Dimensional Real Predual of Lorentz Sequence Space. Mediterr. J. Math. 13, 2827–2839 (2016). https://doi.org/10.1007/s00009-015-0658-4

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  • DOI: https://doi.org/10.1007/s00009-015-0658-4

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