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The unit ball of the space of bilinear forms on $\mathbb{R}^3$ with the supremum norm

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We classify all the extreme and exposed bilinear forms of the unit ball of ${\mathcal L}(^2l_{\infty}^3)$ which leads to a complete formula of $\|f\|$ for every $f\in {{\mathcal L}(^2l_{\infty}^3)}^*$. It follows from this formula that every extreme bilinear form of the unit ball of ${\mathcal L}(^2l_{\infty}^3)$ is exposed.

Abstract

We classify all the extreme and exposed bilinear forms of the unit ball of ${\mathcal L}(^2l_{\infty}^3)$ which leads to a complete formula of $\|f\|$ for every $f\in {{\mathcal L}(^2l_{\infty}^3)}^*$. It follows from this formula that every extreme bilinear form of the unit ball of ${\mathcal L}(^2l_{\infty}^3)$ is exposed.

참고문헌 (31)

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