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Let n ∈ ℕ. An element (x
1, … , xn
) ∈ En
is called a norming point of
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) ∈ En
is called a norming point of T ∈
Norm(T) = {(x 1, … , x n) ∈ En ∶ (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 ∈
Let 𝑛 ≥ 2. A continuous 𝑛-linear form 𝑇 on a Banach space 𝐸 is called norm-peak if there is a unique (𝑥1, … , 𝑥𝑛) ∈ 𝐸𝑛 such that ║𝑥1║ = … = ║𝑥𝑛║ = 1 and for the multilinear operator norm it holds ‖𝑇 ‖ = |𝑇 (𝑥1, … , 𝑥𝑛)|.
Let 0 ≤ 𝜃 ≤
In this note, we characterize all norm-peak multilinear forms on
We classify the extreme 2-homogeneous polynomials on 2 with the hexagonal norm of weight ½. As applications, using its extreme points with the Krein-Milman Theorem, we explicitly compute the polarization and unconditional constants of .
Abstract
and
which answers the questions in [31].