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The norming sets of P(_d∗(², w)_)

Kim Sung Guen

Commentationes Mathematicae

2023

Vol. 61, No. 1/2

25--31

Let n ∈ N. An element x ∈ E is called a norming point of P ∈ P(n E) if YxY = ² and SP(x)S = YPY, where P(n E) denotes the space of all continuous n-homogeneous polynomials on E. For P ∈ P(n E), we define Norm(P) = x ∈ E ∶ x is a norming point of P. Norm(P) is called the norming set of P. We classify Norm(P) for every P ∈ P(_ d∗(², w)_ ), where d∗(², w)_ = R_ with the octagonal norm of weight x < w < ².

Classification of the norming sets of Ls(N l_² )

Kim Sung Guen

Commentationes Mathematicae

2023

Vol. 61, No. 1/2

33--43

Let n ∈ N, n ⩾ _. Let (E, Y ⋅ Y) be a Banach space. An element (x² , . . . , xn ) ∈ En is called a norming point of T ∈ L(n E) if Yx² Y = ⋅ ⋅ ⋅ = Yxn Y = ² and ST(x² , . . . , xn )S = YTY, where L(n E) denotes the space of all continuous symmetric n-linear forms on E. For T ∈ L(n E), we define Norm(T) = (x² , . . . , xn ) ∈ En ∶ (x² , . . . , xn ) is a norming point of T. Norm(T) is called the norming set of T. In this paper, we classify Norm(T) for every T ∈ Ls (N l _ ² ), where Ls (N l _² ) denotes the space of all continuous symmetric N-linear forms on the plane with the l² -norm.

The norming set of a bilinear form on l2∞

Kim Sung Guen

Commentationes Mathematicae

2020

Vol. 60, No. 1/2

37--63

An element (x1,…, xn) ∈ En is called a norming point of T ∈ L(nE) if ∥x1∥ = ⋯ = ∥xn∥ = 1 and ∣T(x1,…, xn)∣ = ∥T∥, where L(nE) denotes the space of all continuous n-linear forms on E. For T ∈ L(nE), we define Norm (T) = {(x1,…, xn) ∈ En: (x1,…, xn) is a norming point of T}. Norm (T) is called the norming set of T. We classify Norm (T) for every T ∈ L(2l2∞).