TY - JOUR AU - Kim, S. G. PY - 2021/06/22 Y2 - 2024/03/28 TI - The norming set of a symmetric bilinear form on the plane with the supremum norm JF - Matematychni Studii JA - Mat. Stud. VL - 55 IS - 2 SE - Articles DO - 10.30970/ms.55.2.171-180 UR - http://matstud.org.ua/ojs/index.php/matstud/article/view/152 SP - 171-180 AB - An element $(x_1, \ldots, x_n)\in E^n$ is called a {\em norming point} of $T\in {\mathcal L}_s(^n E)$ if $\|x_1\|=\cdots=\|x_n\|=1$ and$|T(x_1, \ldots, x_n)|=\|T\|,$ where ${\mathcal L}_s(^n E)$ denotes the space of all symmetric continuous $n$-linear forms on $E.$For $T\in {\mathcal L}_s(^n E),$ we define $$\mathop{\rm Norm}(T)=\{(x_1, \ldots, x_n)\in E^n: (x_1, \ldots, x_n)~\mbox{is a norming point of}~T\}.$$$\mathop{\rm Norm}(T)$ is called the {\em norming set} of $T$. We classify $\mathop{\rm Norm}(T)$ for every $T\in {\mathcal L}_s(^2l_{\infty}^2)$. ER -