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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.