Mathematica Pannonica
Volume/Issue:
Volume 29_NS3: Issue 1
The Norming Sets of Multilinear Forms on the Plane with a Certain Norm
Author:
Sung Guen Kim Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea

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Pages:
120–126
Online Publication Date:
24 Apr 2023
Publication Date:
19 May 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2023.00011
Keywords:
Norming points; multilinear forms of the plane with a certain norm
Open access

Let n ∈ ℕ. An element (x1, … , xn) ∈ En is called a norming point of T∈LnE if x1=⋯=xn=1 and Tx1,…,xn=T, where LnE denotes the space of all continuous symmetric n-linear forms on E. For T∈LnE, we define

NormT=x1,…,xn∈En:x1,…,xn is a norming of T.

Norm(T) is called the norming set of T.

Let ℝ·2 be the plane with a certain norm such that the set of the extreme points of its unit ball ext Bℝ·2=±W1,±W2 for some W1≠±W2∈ℝ·2.

In this paper, we classify Norm(T) for every T∈Lnℝ·2. We also present relations between the norming sets of Lnl∞2 and Lnl12.

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  • [6]

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

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

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    KIM, S. G. The norming set of a symmetric bilinear form on the plane with the supremum norm, Mat. Stud. 55, 2 (2021), 171–180.

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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 l 1 2  and  L s 2 l 1 3, 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 2 ℝ h w 2, to appear in Acta Sci. Math. (Szeged) 89, 3–4 (2023)

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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:

  • 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

Advisory Board

  • 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
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
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Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
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ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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