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The norming set of a symmetric 3-linear form on the plane with the $l_1$-norm
Author(s) -
Sung Guen Kim
Publication year - 2021
Publication title -
new zealand journal of mathematics
Language(s) - English
Resource type - Journals
eISSN - 1179-4984
pISSN - 1171-6096
DOI - 10.53733/177
Subject(s) - norm (philosophy) , combinatorics , mathematics , discrete mathematics , philosophy , epistemology
An element $(x_1, \ldots, x_n)\in E^n$ is called a {\em norming point} of $T\in {\mathcal L}(^n E)$ if $\|x_1\|=\cdots=\|x_n\|=1$ and$|T(x_1, \ldots, x_n)|=\|T\|,$ where ${\mathcal L}(^n E)$ denotes the space of all continuous $n$-linear forms on $E.$For $T\in {\mathcal L}(^n E),$ we define $${Norm}(T)=\Big\{(x_1, \ldots, x_n)\in E^n: (x_1, \ldots, x_n)~\mbox{is a norming point of}~T\Big\}.$$${Norm}(T)$ is called the {\em norming set} of $T$. We classify ${Norm}(T)$ for every $T\in {\mathcal L}_s(^3 l_{1}^2)$.