The norming sets of P(_d∗(², w)_)

• Autorzy: Kim Sung Guen

Identyfikatory

DOI

10.14708/cm.v61i1-2.7148

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

norming points; 2-homogeneous polynomials; plane with octagonal norm

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2023
• Tom: Vol. 61, No. 1/2
• Strony: 25--31
• Opis fizyczny: Bibliogr. 8 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) 172 (1995), 19-28.
• [2] R. M. Aron and M. Klimek, Supremum norms for quadratic polynomials, Arch. Math. 76 (2001), 73-80, DOI 10.1007/s000130050544.
• [3] E. Bishop and 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.
• [4] Y. S. Choi and S. G. Kim, Norm or numerical radius attaining multilinear mappings and polynomials, J. Lon don Math. Soc. 54 (1996), 135-147, DOI 10.1112/jlms/54.1.135.
• [5] S. Dineen, Complex analysis on infinite-dimensional spaces, Springer-Verlag, London 1999, DOI 10.1007/978-1-4471-0869-6.
• [6] M. Jimenez Sevilla and R. Paya, Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces, Studia Math. 127 (1998), 99-112, DOI 10.4064/sm-127-2-99-112.
• [7] S. G. Kim, Fe unit ball of P( 2d∗(1,w) 2 ), Math. Proc. R. Ir. Acad. 111 (2011), no. 2, 79-94, DOI 10.3318/pria.2011.111.1.9.
• [8] 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.