Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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THE NORMING SET OF A POLYNOMIAL IN 𝒫(2𝑙2∞)

  • Kim, Sung Guen (Department of Mathematics, Kyungpook National University)
  • Received : 2019.12.26
  • Accepted : 2020.06.25
  • Published : 2020.09.25
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Abstract

An element x ∈ E is called a norming point of P ∈ P(nE) if ║x║ = 1 and |P(x)| = ║P║. For P ∈ P(nE), 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 P ∈ 𝒫(2𝑙2∞).

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References

  1. R.M. Aron, C. Finet and E. Werner, 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. E. Bishop and R. Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc. 67 (1961), 97-98. https://doi.org/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. (2) 54 (1996), 135-147. https://doi.org/10.1112/jlms/54.1.135
  4. Y.S. Choi and S.G. Kim, The unit ball of P($^2l^2_2$), Arch. Math. (Basel) 71 (1998), 472-480. https://doi.org/10.1007/s000130050292
  5. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London (1999).
  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.