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Another characterization of the norming set of $T\in {\mathcal L}(^2l_{\infty}^2)$

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In this paper we present another characterization of the \linebreak norming set of $T\in {\mathcal L}(^2l_{\infty}^2)$ in terms of $\qopname\relax o{Norm}(T)\cap \Omega$ whose proofs are more systematic than those of Kim \cite{K1}, where $\Omega=\big\{\big((1, 1), (1, 1)\big)$, $\big((1, 1), (1, -1)\big)$, $\big((1, -1), (1, 1)\big)$, $\big((1, -1), (1, -1)\big)\big\}$.

Abstract

In this paper we present another characterization of the \linebreak norming set of $T\in {\mathcal L}(^2l_{\infty}^2)$ in terms of $\qopname\relax o{Norm}(T)\cap \Omega$ whose proofs are more systematic than those of Kim \cite{K1}, where $\Omega=\big\{\big((1, 1), (1, 1)\big)$, $\big((1, 1), (1, -1)\big)$, $\big((1, -1), (1, 1)\big)$, $\big((1, -1), (1, -1)\big)\big\}$.

참고문헌 (10)

  1. R. M. Aron, "Function spaces", pp.19~28 (1995), Dekker
  2. Errett Bishop, "A proof that every Banach space is subreflexive", Bulletin of the American Mathematical Society, 67(1), pp.97~98 (1961), American Mathematical Society (AMS)[DOI]
  3. Yun Sung Choi, "Norm or Numerical Radius Attaining Multilinear Mappings and Polynomials", Journal of the London Mathematical Society, 54(1), pp.135~147 (1996), Wiley[DOI]
  4. S. Dineen, "Complex analysis on innite-dimensional spaces" (1999), Springer-Verlag London, Ltd.
  5. M. Jimenéz Sevilla, "Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces", Studia Mathematica, 127(2), pp.99~112 (1998), Institute of Mathematics, Polish Academy of Sciences[DOI]
  6. S. G. Kim, "The norming set of a bilinear form on l2∞", Comment. Math, 60(1-2), pp.37~63 (2020)
  7. 김성권, "The norming set of a polynomial in ${\mathcal P}(^2l_{\infty}^2)$", 호남수학학술지, 42(3), pp.569~576 (2020), 호남수학회
  8. S. G. Kim, "The norming set of a symmetric bilinear form on the plane with the supremum norm", Matematychni Studii, 55(2), pp.171~180 (2021), Ivan Franko National University of Lviv[DOI]
  9. S. G. Kim, "The norming set of a bilinear form on the plane with the l1-norm"
  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, pp.95~108 (2021)

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