Author:
Sung Guen Kim Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea

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Let 𝑛 ∈ ℕ. An element (x1, … , x𝑛) ∈ En is called a norming point of TL(nE) if ‖x1‖ = ⋯ = ‖xn‖ = 1 and |T (x1, … , xn)| = ‖T‖, where L (nE) denotes the space of all continuous n-linear forms on E. For TL(nE), we define

Norm(T) = {(x1, … , xn) ∈ En ∶ (x1, … , xn) is a norming point of T}.

Norm(T) is called the norming set of T. We classify Norm(T) for every TL(2𝑑(1, w)2), where 𝑑(1, w)2 = ℝ2 with the octagonal norm of weight 0 < w < 1 endowed with x,yd*1,w=maxx,y,x+y1+w.

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    Aron, R. M., Finet, C., and 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.

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  • [2]

    Bishop, E. and Phelps, R. A proof that every Banach space is subreflexive. Bull. Amer. Math. Soc. 67 (1961), 9798.

  • [3]

    Choi, Y. S. and Kim, S. G. Norm or numerical radius attaining multilinear mappings and polynomials. J. London Math. Soc. (2) 54 (1996), 135147.

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  • [4]

    Dineen, S. Complex Analysis on Infinite Dimensional Spaces. Springer-Verlag, London (1999).

  • [5]

    Jiménez Sevilla, M. and Payá, R. Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces. Studia Math. 127 (1998), 99112.

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  • [6]

    Kim, S. G. The norming set of a polynomial in P(2 𝑙2 ). Honam Math. J. 42 3 (2020), 569576.

  • [7]

    Kim, S. G. The norming set of a bilinear form on 𝑙2 . Comment. Math. 60 1-2 (2020), 3763.

  • [8]

    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), 95108.

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    Kim, S. G. The norming sets of L(2 𝑙2 1) and L𝑠(2 𝑙31). Bull. Transilv. Univ. Brasov, Ser. III: Math. Comput. Sci. 64 (2) (2022), 125150.

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  • [10]

    Kim, S. G. The norming sets of L(22 ℎ(w)). Acta Sci. Math. (Szeged), 89 (1-2) (2023), 6179.

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Editor in Chief: László TÓTH (University of Pécs)

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  • János PINTZ (Rényi Institute of Mathematics, Budapest, Hungary)
  • Ferenc SCHIPP (Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary)
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  • István BERKES (Rényi Institute of Mathematics, Budapest, Hungary)
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Mathematica Pannonica
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