Norm attaining bilinear forms on the plane with the l1-norm

Abstract

For given unit vectors x1, · · ·, xn of a real Banach space E, we define NA(ℒ(nE))(x1,…xn)={T∈ℒ(nE):|T(x1,…xn)|=‖T‖=1},NA\left( {\mathcal{L}\left( {^nE} \right)} \right)\left( {{x_1}, \ldots {x_n}} \right) = \left\{ {T \in \mathcal{L}\left( {^nE} \right):\left| {T\left( {{x_1}, \ldots {x_n}} \right)} \right| = \left\| T \right\| = 1} \right\}, where ℒ(nE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm ||T|| = sup||xk||=1,1≤k≤n |T(x1, . . ., xn)|.

Keywords

• norm attaining bilinear forms
• 46a22