Mathematica Pannonica
Volume/Issue:
Volume 29_NS3: Issue 2
The Norming Sets of L(2d*(1, w)2)
Author:
Sung Guen Kim Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea

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Pages:
219–229
Online Publication Date:
08 Nov 2023
Publication Date:
07 Dec 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2023.00022
Keywords:
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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Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752

Editor in Chief: László TÓTH, University of Pécs, Pécs, Hungary

Honorary Editors in Chief:

  • † István GYŐRI, University of Pannonia, Veszprém, Hungary
  • János PINTZ, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Ferenc SCHIPP, Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary
  • Sándor SZABÓ, University of Pécs, Pécs, Hungary
     

Deputy Editors in Chief:

  • Erhard AICHINGER, JKU Linz, Linz, Austria
  • Ferenc HARTUNG, University of Pannonia, Veszprém, Hungary
  • Ferenc WEISZ, Eötvös Loránd University, Budapest, Hungary

Editorial Board

  • Attila BÉRCZES, University of Debrecen, Debrecen, Hungary
  • István BERKES, Rényi Institute of Mathematics, Budapest, Hungary
  • Károly BEZDEK, University of Calgary, Calgary, Canada
  • György DÓSA, University of Pannonia, Veszprém, Hungary
  • Balázs KIRÁLY – Managing Editor, University of Pécs, Pécs, Hungary
  • Vedran KRCADINAC, University of Zagreb, Zagreb, Croatia 
  • Željka MILIN ŠIPUŠ, University of Zagreb, Zagreb, Croatia
  • Gábor NYUL, University of Debrecen, Debrecen, Hungary
  • Margit PAP, University of Pécs, Pécs, Hungary
  • István PINK, University of Debrecen, Debrecen, Hungary
  • Mihály PITUK, University of Pannonia, Veszprém, Hungary
  • Lukas SPIEGELHOFER, Montanuniversität Leoben, Leoben, Austria
  • Andrea ŠVOB, University of Rijeka, Rijeka, Croatia
  • Csaba SZÁNTÓ, Babeş-Bolyai University, Cluj-Napoca, Romania
  • Jörg THUSWALDNER, Montanuniversität Leoben, Leoben, Austria
  • Zsolt TUZA, University of Pannonia, Veszprém, Hungary

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  • Szilárd RÉVÉSZ – Chair, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Gabriella BÖHM
  • György GÁT, University of Debrecen, Debrecen, Hungary

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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)
ISSN 0865-2090 (Print)

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