Research Article
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Year 2022, , 1 - 6, 14.03.2022
https://doi.org/10.33205/cma.981877

Abstract

References

  • M. D. Acosta, J. L. Dávila: A basis of $\mathbb{R}^n$ with good isometric properties and some applications to denseness of norm attaining operators, J. Funct. Anal., 279 (6) (2020), 108602, 26 pp.
  • 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).
  • E. Bishop, R. Phelps: A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc., 67 (1961), 97–98.
  • Y. S. Choi, S. G. Kim: Norm or numerical radius attaining multilinear mappings and polynomials, J. London Math. Soc., 54 (1) (1996), 135–147.
  • S. Dantas, M. Jung, O. Roldán and A. R. Zoca: Norm-attaining tensors and nuclear operators, to appear in Mediterr. J. Math. (2022). DOI: https://doi.org/10.1007/s00009-021-01949-5
  • S. Dineen: Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London, (1999).
  • M. Jimenez Sevilla, R. Paya: Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces, Studia Math., 127 (1998), 99–112.
  • S. G. Kim: The geometry of ${\mathcal L}(^2l_{\infty}^2)$, Kyungpook Math. J., 58 (2018), 47–54.
  • S. G. Kim: The norming set of a polynomial in ${\mathcal P}(^2 l_{\infty}^2),$ , Honam Math. J., 42 (3) (2020), 569-576.
  • S. G. Kim: The norming set of a symmetric bilinear form on the plane with the supremum norm, Mat. Stud., 55 (2) (2021), 171–180.

Norm attaining multilinear forms on the spaces $c_0$ or $l_1$

Year 2022, , 1 - 6, 14.03.2022
https://doi.org/10.33205/cma.981877

Abstract

TL(nE)T∈L(nE) is called a norming attaining if there are x1,,xnEx1,…,xn∈E such that x1==xn=1‖x1‖=⋯=‖xn‖=1 and |T(x1,,xn)|=T,|T(x1,…,xn)|=‖T‖, where L(nE)L(nE) denotes the space of all continuous nn-linear forms on E.E. We investigate norm attaining multilinear forms on c0c0 or l1.l1.

References

  • M. D. Acosta, J. L. Dávila: A basis of $\mathbb{R}^n$ with good isometric properties and some applications to denseness of norm attaining operators, J. Funct. Anal., 279 (6) (2020), 108602, 26 pp.
  • 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).
  • E. Bishop, R. Phelps: A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc., 67 (1961), 97–98.
  • Y. S. Choi, S. G. Kim: Norm or numerical radius attaining multilinear mappings and polynomials, J. London Math. Soc., 54 (1) (1996), 135–147.
  • S. Dantas, M. Jung, O. Roldán and A. R. Zoca: Norm-attaining tensors and nuclear operators, to appear in Mediterr. J. Math. (2022). DOI: https://doi.org/10.1007/s00009-021-01949-5
  • S. Dineen: Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London, (1999).
  • M. Jimenez Sevilla, R. Paya: Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces, Studia Math., 127 (1998), 99–112.
  • S. G. Kim: The geometry of ${\mathcal L}(^2l_{\infty}^2)$, Kyungpook Math. J., 58 (2018), 47–54.
  • S. G. Kim: The norming set of a polynomial in ${\mathcal P}(^2 l_{\infty}^2),$ , Honam Math. J., 42 (3) (2020), 569-576.
  • S. G. Kim: The norming set of a symmetric bilinear form on the plane with the supremum norm, Mat. Stud., 55 (2) (2021), 171–180.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sung Guen Kim 0000-0001-8957-3881

Publication Date March 14, 2022
Published in Issue Year 2022

Cite

APA Kim, S. G. (2022). Norm attaining multilinear forms on the spaces $c_0$ or $l_1$. Constructive Mathematical Analysis, 5(1), 1-6. https://doi.org/10.33205/cma.981877
AMA Kim SG. Norm attaining multilinear forms on the spaces $c_0$ or $l_1$. CMA. March 2022;5(1):1-6. doi:10.33205/cma.981877
Chicago Kim, Sung Guen. “Norm Attaining Multilinear Forms on the Spaces $c_0$ or $l_1$”. Constructive Mathematical Analysis 5, no. 1 (March 2022): 1-6. https://doi.org/10.33205/cma.981877.
EndNote Kim SG (March 1, 2022) Norm attaining multilinear forms on the spaces $c_0$ or $l_1$. Constructive Mathematical Analysis 5 1 1–6.
IEEE S. G. Kim, “Norm attaining multilinear forms on the spaces $c_0$ or $l_1$”, CMA, vol. 5, no. 1, pp. 1–6, 2022, doi: 10.33205/cma.981877.
ISNAD Kim, Sung Guen. “Norm Attaining Multilinear Forms on the Spaces $c_0$ or $l_1$”. Constructive Mathematical Analysis 5/1 (March 2022), 1-6. https://doi.org/10.33205/cma.981877.
JAMA Kim SG. Norm attaining multilinear forms on the spaces $c_0$ or $l_1$. CMA. 2022;5:1–6.
MLA Kim, Sung Guen. “Norm Attaining Multilinear Forms on the Spaces $c_0$ or $l_1$”. Constructive Mathematical Analysis, vol. 5, no. 1, 2022, pp. 1-6, doi:10.33205/cma.981877.
Vancouver Kim SG. Norm attaining multilinear forms on the spaces $c_0$ or $l_1$. CMA. 2022;5(1):1-6.