The norming set of a symmetric bilinear form on the plane with the supremum norm

  • S. G. Kim Department of Mathematics, Kyungpook National University, Republic of Korea
Keywords: norming points;, symmetric bilinear forms

Abstract

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 $T\in {\mathcal L}_s(^2l_{\infty}^2)$.

References

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Published
2021-06-22
How to Cite
1.
Kim SG. The norming set of a symmetric bilinear form on the plane with the supremum norm. Mat. Stud. [Internet]. 2021Jun.22 [cited 2021Sep.17];55(2):171-80. Available from: http://matstud.org.ua/ojs/index.php/matstud/article/view/152
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Articles