The norming set of a bilinear form on l2∞

• Autorzy: Kim Sung Guen

Identyfikatory

DOI

10.14708/cm.v60i1–2.7071

• Języki publikacji: EN

Abstrakty

EN

An element (x₁,…, x_n) ∈ Eⁿ is called a norming point of T ∈ L(ⁿE) if ∥x₁∥ = ⋯ = ∥x_n∥ = 1 and ∣T(x₁,…, x_n)∣ = ∥T∥, where L(ⁿE) denotes the space of all continuous n-linear forms on E. For T ∈ L(ⁿE), we define Norm (T) = {(x₁,…, x_n) ∈ Eⁿ: (x₁,…, x_n) is a norming point of T}. Norm (T) is called the norming set of T. We classify Norm (T) for every T ∈ L(²l²_∞).

Słowa kluczowe

EN

norming points; bilinear forms; Banach space

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2020
• Tom: Vol. 60, No. 1/2
• Strony: 37--63
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Kim Sung Guen

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

Bibliografia

• [1] R. M. Aron, C. Finet, and E. Werner, Some remarks on norm-attaining n-linear forms, Function spacer (Edwardsville, IL, 1994), Lecture Notes in Pure and Appl. Math., vol. 172, Dekker, New York, 1995, 19-28.
• [2] E. Bishop and R. R. Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc. 67 (1961), 97-98, DOI 10.1090/S0002-9904-1961-10514-4.
• [3] Y. S. Choi and S. G. Kim, Norm or numerical radius attaining multilinear mappings and polynomials, J. London Math. Soc. 54 (1996), no. 1, 135-147, DOI 10.1112/jlms/54.1.135.
• [4] S. Dineen, Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London 1999, DOI 10.1007/978-1-4471-0869-6.
• [5] M. Jiménez Sevilla and R. Payá, Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces, Studia Math. 127 (1998), no. 2, 99-112, DOI 10.4064/sm-127-2-99-112.
• [6] S. G. Kim, The unit ball of Ls (2l2∞), Extracta Math. 24 (2009), no. 1, 17-29.
• [7] S. G. Kim, The geometry of L (2l2∞), Kyungpook Math. J. 58 (2018), no. 1, 47-54, DOI 10.5666/KMJ.2018.58.1.47.
• [8] S. G. Kim, The norming set of a polynomial in P(2l2∞), Honam Math. J. 42 (2020), no. 3, 569-576, DOI 10.5831/HMJ.2020.42.3.569.
• [9] S. G. Kim, The norming set of a symmetric bilinear form on the plane with the supremum norm, preprint.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).