대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제37권4호
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  • Pages.1131-1146
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  • 2022
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ANOTHER CHARACTERIZATION OF THE NORMING SET OF T ∈ 𝓛(2𝒍2∞)

  • Kim, Sung Guen (Department of Mathematics Kyungpook National University)
  • 투고 : 2021.11.18
  • 심사 : 2022.01.14
  • 발행 : 2022.10.01
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초록

In this paper we present another characterization of the norming set of T ∈ 𝓛(2𝒍2∞) in terms of Norm(T) ∩ Ω whose proofs are more systematic than those of Kim [6], where Ω = {((1, 1), (1, 1)), ((1, 1), (1, -1)), ((1, -1), (1, 1)), ((1, -1), (1, -1))}.

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참고문헌

  1. R. M. Aron, C. Finet, and E. Werner, Some remarks on norm-attaining n-linear forms, in Function spaces (Edwardsville, IL, 1994), 19-28, Lecture Notes in Pure and Appl. Math., 172, Dekker, New York, 1995.
  2. E. Bishop and R. 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), no. 1, 135-147. https://doi.org/10.1112/jlms/54.1.135
  4. S. Dineen, Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 1999. https://doi.org/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), no. 2, 99-112. https://doi.org/10.4064/sm-127-2-99-112
  6. S. G. Kim, The norming set of a bilinear form on l2∞, Comment. Math. 60 (2020), no. 1-2, 37-63.
  7. S. G. Kim, The norming set of a polynomial in P(2l2∞), Honam Math. J. 42 (2020), no. 3, 569-576. https://doi.org/10.5831/HMJ.2020.42.3.569
  8. S. G. Kim, The norming set of a symmetric bilinear form on the plane with the supremum norm, Mat. Stud. 55 (2021), no. 2, 171-180. https://doi.org/10.30970/ms.55.2.171-180
  9. S. G. Kim, The norming set of a bilinear form on the plane with the l1-norm, Preprint.
  10. S. G. Kim, The norming set of a symmetric 3-linear form on the plane with the l1-norm, New Zealand J. Math. 51 (2021), 95-108. https://doi.org/10.53733/177