Norm attaining bilinear forms on the plane with the octagonal norm

• Autorzy: Kim Sung Guen

Identyfikatory

DOI

10.14708/cm.v61i1-2.7128

• Języki publikacji: EN

Abstrakty

EN

For given unit vectors x² , ⋯, xn of a real Banach space E, we define NAL(n E)(x² , . . . , xn ) = T ∈ L(n E) ∶ ST(x² , . . . , xn )S = YTY = ², where L(n E) denotes the Banach space of all continuous n-linear forms on E endowed with the norm YTY = sup{ST(x² , . . . , xn )S ∶ Yxk Y = ², ² ⩽ k ⩽ n}. In this paper, we classify NA(L(_ R_ o(w)))((x² , x_ ), (y² , y_ )) for unit vectors (x² , x_ ), (y² , y_ ) ∈ R_ o(w) , where R_ o(w) = R_ with the octagonal norm with weight x < w < ²For given unit vectors x² , ⋯, xn of a real Banach space E, we define NAL(n E)(x² , . . . , xn ) = T ∈ L(n E) ∶ ST(x² , . . . , xn )S = YTY = ², where L(n E) denotes the Banach space of all continuous n-linear forms on E endowed with the norm YTY = sup{ST(x² , . . . , xn )S ∶ Yxk Y = ², ² ⩽ k ⩽ n}. In this paper, we classify NA(L(_ R_ o(w)))((x² , x_ ), (y² , y_ )) for unit vectors (x² , x_ ), (y² , y_ ) ∈ R_ o(w) , where R_ o(w) = R_ with the octagonal norm with weight x < w < ².

Słowa kluczowe

EN

norm attaining bilinear; forms

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2023
• Tom: Vol. 61, No. 1/2
• Strony: 15--24
• 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), Lecture Notes in Pure and Appl. Math., vol. 172, Dekker, New York, 1995, 19–28.
• [2] 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.
• [3] 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.
• [4] S. Dineen, Complex analysis on infinite-dimensional spaces, Springer-Verlag, London 1999, DOI 10.1007/978-1-4471-0869-6.
• [5] 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.
• [6] S. G. Kim, Explicit norm attaining polynomials, Indian J. Pure Appl. Math. 34 (2003), 523–527.
• [7] S. G. Kim, Geometry of bilinear forms on the plane with the octagonal norm, Bull. Transilv. Univ. Brasov Ser. III. Math. and Comput. Sci. 63 (2021), no. 1, 161–189, DOI 10.31926/but.mif.
• [8] S. G. Kim, Norm attaining bilinear forms on the plane with the l1-norm, Acta Univ. Sapientiae Math. 14 (2022), no. 1, 115–124, DOI 10.2478/ausm-2022-0008.