Mathematica Pannonica
Volume/Issue:
Accepted Manuscript / Online First
The Norming Sets of L (2 d *(1, w)2)
Author:
Sung Guen Kim Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea

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Online Publication Date:
08 Nov 2023
Publication Date:
08 Nov 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2023.00022
Keywords (English):
Norming points; bilinear forms; the plane with the octagonal norm
Open access

Let 𝑛 ∈ ℕ. An element (x1, … , x𝑛) ∈ En is called a norming point of T ∈ L(nE) if ‖x1‖ = ⋯ = ‖xn‖ = 1 and |T (x1, … , xn)| = ‖T‖, where L (nE) denotes the space of all continuous n-linear forms on E. For T ∈ L(nE), we define

Norm(T) = {(x1, … , xn) ∈ En ∶ (x1, … , xn) is a norming point of T}.

Norm(T) is called the norming set of T. We classify Norm(T) for every T ∈ L(2𝑑∗(1, w)2), where 𝑑∗(1, w)2 = ℝ2 with the octagonal norm of weight 0 < w < 1 endowed with x,yd*1,w=maxx,y,x+y1+w.

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    Kim, S. G. The norming set of a polynomial in P(2 𝑙2 ∞). Honam Math. J. 42 3 (2020), 569–576.

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    Kim, S. G. The norming set of a bilinear form on 𝑙2 ∞. Comment. Math. 60 1-2 (2020), 37–63.

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    Kim, S. G. The norming set of a symmetric 3-linear form on the plane with the 𝑙1-norm. New Zealand J. Math. 51 (2021), 95–108.

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    Kim, S. G. The norming sets of L(2 𝑙2 1) and L𝑠(2 𝑙31). Bull. Transilv. Univ. Brasov, Ser. III: Math. Comput. Sci. 64 (2) (2022), 125–150.

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    Kim, S. G. The norming sets of L(2ℝ2 ℎ(w)). Acta Sci. Math. (Szeged), 89 (1-2) (2023), 61–79.

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Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752
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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • Attila BÉRCZES (University of Debrecen)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • György DÓSA (University of Pannonia, Veszprém)
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  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Gábor NYUL (University of Debrecen)
  • Margit PAP (University of Pécs)
  • István PINK (University of Debrecen)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

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  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM
  • György GÁT (University of Debrecen)

University of Pécs,
Faculty of Sciences,
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Department of Mathematics
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ltoth@gamma.ttk.pte.hu

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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
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ISSN 2786-0752 (Online)
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