The norming set of a bilinear form on $l_{\infty}^2$

Sung Guen Kim

Commentationes Mathematicae, Tome 60 (2020) no. 1-2, pp. 37-63.

Résumé

An element \((x_1, \ldots, x_n)\in E^n\) is called a~\emph{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 \(\qopname\relax o{Norm}(T)=\{(x_1, \ldots, x_n)\in E^n: (x_1, \ldots, x_n)\text{~is a~norming point of~}T\}\). \(\qopname\relax o{Norm}(T)\) is called the \emph{norming set} of \(T\). We classify \(\qopname\relax o{Norm}(T)\) for every \(T\in {\mathcal L}(^2l_{\infty}^2)\).

Détail

DOI : 10.14708/cm.v60i1-2.7071

Classification : 46A22
Mots-clés : Norming points, bilinear forms