Norm attaining multilinear forms on the spaces $c_0$ or $l_1$
Norm attaining multilinear forms on the spaces $c_0$ or $l_1$
T∈L(nE)T∈L(nE) is called a norming attaining if there are x1,…,xn∈Ex1,…,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.
___
- 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.
- ISSN: 2651-2939
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2018
- Yayıncı: Tuncer ACAR