The norming sets of multilinear forms on R² with a rotated supremum norm

• Autorzy: Kim Sung Guen

Identyfikatory

DOI

10.21008/j.0044-4413.2024.0005

• Języki publikacji: EN

Abstrakty

EN

Let n ∈ N, n ≥ 2. An element (x₁,…, x_n) ∈ E_n 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 form 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. Let 0 ≤ θ < π/4 and ℓ²_(∞,θ) = R² with the rotated supremum norm ∥(x, y)∥_(∞,θ) = max{|x cos θ + y sin θ|, |x sin θ − y cos θ|}. In this paper, we characterize Norm(T) for every T ∈ L(^mℓ²_(∞,θ)) for m ≥ 2.

Słowa kluczowe

EN

norming points; multilinear forms

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2024
• Tom: nr 67
• Strony: 49--63
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Kim Sung Guen

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

Bibliografia

• [1] Aron R. M., Finet C., Werner E., Some remarks on norm-attaining n-linear forms, Function spaces (Edwardsville, IL, 1994), 19-28, Lecture Notes in Pure and Appl. Math., 172, Dekker, New York, 1995.
• [2] Bishop E., Phelps R., A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc., 67 (1961), 97-98.
• [3] Choi Y. S., Kim S. G., Norm or numerical radius attaining multilinear mappings and polynomials, J. London Math. Soc., 54(2) (1996), 135-147.
• [4] Dineen S., Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London, 1999.
• [5] Jiménez Sevilla M., Payá R., Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces, Studia Math., 127 (1998), 99-112.
• [6] Kim S. G., The norming set of a bilinear form on l2∞ , Comment. Math., 60 (1-2) (2020), 37-63.
• [7] Kim S. G., The norming set of a polynomial in P(2l2∞), Honam Math. J., 42(3) (2020), 569-576.
• [8] Kim S. G., The norming set of a symmetric bilinear form on the plane with the supremum norm, Mat. Stud., 55(2) (2021), 171-180.
• [9] Kim S. G., The norming set of a symmetric 3-linear form on the plane with the l1-norm, New Zealand J. Math., 51 (2021), 95-108.
• [10] Kim S. G., The unit ball of bilinear forms on R2 with a rotated supremum norm, Bull. Transilv. Univ. Brasov, Ser. III: Math. Comput. Sci., 2(64)(1) (2022), 99-120.
• [11] Kim S. G., The norming sets of L(2l21) and Ls(2l31), Bull. Transilv. Univ. Brasov, Ser. III: Math. Comput. Sci., 2(64)(2) (2022), 125-150.
• [12] Kim S. G., The norming sets of L(2R2h(w)), Acta Sci. Math. (Szeged), 89(1-2) (2023), 61-79.