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Let *n* ∈ ℕ. An element (*x*
_{1}, … , *x _{n}
*) ∈

*E*is called a

^{n}*norming point*of

*n*-linear forms on

*E*. For

Norm(*T*) is called the *norming set* of *T*.

Let

In this paper, we classify Norm(*T*) for every

Let *𝑛* ∈ ℕ. An element (*x*
_{1}, … , *x*
_{𝑛}) ∈ *E ^{n}
* is called a

*norming point*of

*T*∈

*) if ‖*

^{n}E*x*

_{1}‖ = ⋯ = ‖

*x*‖ = 1 and |

_{n}*T*(

*x*

_{1}, … ,

*x*)| = ‖

_{n}*T*‖, where

*) denotes the space of all continuous*

^{n}E*n*-linear forms on

*E*. For

*T*∈

*), we define*

^{n}ENorm(*T*) = {(*x*
_{1}, … , *x*
_{n}) ∈ *E ^{n}
* ∶ (

*x*

_{1}, … ,

*x*

_{n}) is a norming point of

*T*}.

Norm(*T*) is called the *norming set* of *T*. We classify Norm(*T*) for every *T* ∈ ^{2}
*𝑑*
_{∗}(1, *w*)^{2}), where *𝑑*
_{∗}(1, *w*)^{2} = ℝ^{2} with the octagonal norm of weight 0 < *w* < 1 endowed with

Let 𝑛 ≥ 2. A continuous 𝑛-linear form 𝑇 on a Banach space 𝐸 is called *norm-peak* if there is a unique (𝑥_{1}, … , 𝑥_{𝑛}) ∈ 𝐸^{𝑛} such that ║𝑥_{1}║ = … = ║𝑥_{𝑛}║ = 1 and for the multilinear operator norm it holds ‖𝑇 ‖ = |𝑇 (𝑥_{1}, … , 𝑥_{𝑛})|.

Let 0 ≤ 𝜃 ≤ ^{2} with the rotated supremum norm ‖(𝑥, 𝑦)‖_{(∞,𝜃)} = max {|𝑥 cos 𝜃 + 𝑦 sin 𝜃|, |𝑥 sin 𝜃 − 𝑦 cos 𝜃|}.

In this note, we characterize all norm-peak multilinear forms on ^{2} with the 𝓁_{𝑝}-norm for 𝑝 = 1, ∞.