Browse > Article
http://dx.doi.org/10.4134/CKMS.c210386

ANOTHER CHARACTERIZATION OF THE NORMING SET OF T ∈ 𝓛(2𝒍2∞)  

Kim, Sung Guen (Department of Mathematics Kyungpook National University)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.4, 2022 , pp. 1131-1146 More about this Journal
Abstract
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))}.
Keywords
Norming points; bilinear forms;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 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   DOI
2 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   DOI
3 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   DOI
4 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   DOI
5 S. G. Kim, The norming set of a bilinear form on l2∞, Comment. Math. 60 (2020), no. 1-2, 37-63.
6 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   DOI
7 S. G. Kim, The norming set of a bilinear form on the plane with the l1-norm, Preprint.
8 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.   DOI
9 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   DOI
10 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.