Classification of the norming sets of Ls(N l_² )

• Autorzy: Kim Sung Guen

Identyfikatory

DOI

10.14708/cm.v61i1-2.7176

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

norming points; symmetric 3-linear forms on on the plane with the l1-norm

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2023
• Tom: Vol. 61, No. 1/2
• Strony: 33--43
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Kim Sung Guen

• Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea

Bibliografia

• [1] R. M. Aron, C. Finet, and E. Werner, Some remarks on norm-attaining n-linear forms, Function spaces (Edwardsville, IL, 1994), Lecture Notes in Pure and Appl. Math., vol. 172, Dekker, New York, 1995, 19-28.
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• [4] S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London 1999, DOI 10.1007/978-1-4471-0869-6.
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• [6] S. G. Kim, Fe norming set of a bilinear form on l 2 ∞, Comment. Math. 60 (2020), no. 1-2, 37-63.
• [7] S. G. Kim, Fe norming set of a polynomial in P( 2 l 2 ∞), Honam Math. J. 42 (2020), no. 3, 569-576, DOI 10.5831/HMJ.2020.42.3.569.
• [8] S. G. Kim, Fe norming set of a symmetric bilinear form on the plane with the supremum norm, Mat. Stud. 55 (2021), no. 2, 171-180, DOI 10.30970/ms.55.2.171-180.
• [9] S. G. Kim, Fe norming set of a symmetric 3-linear form on the plane with the l1-norm, New Zealand J. Math. 51 (2021), 95-108, DOI 10.53733/177.
• [10] S. G. Kim, Fe norming sets of L( 2 l 2 1 ) and Ls( 2 l 3 1 ), Bull. Transilv. Univ. Brasov, Ser. III: Math. Comput. Sci. 2(64) (2022), no. 2, 125-150.
• [11] S. G. Kim, Fe norming sets of L( 2R 2 h(w) ), Acta Sci. Math. (Szeged) 89 (2023), no. 1–2, 61-79, DOI 10.1007/s44146-023-00078-7.
• [12] S. G. Kim, Fe norming sets of L( nR 2 ∥⋅∥ ), preprint.