Mathematica Pannonica
Volume/Issue:
Volume 30_NS4: Issue 2
Norm-Peak Multilinear Forms on the Plane with the Rotated Supremum Norm
Author:
Sung Guen Kim Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea

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Pages:
116–121
Online Publication Date:
23 Sep 2024
Publication Date:
18 Dec 2024
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2024.00012
Keywords:
Norming points; Norm-peak multilinear forms
Open access

Let 𝑛 β‰₯ 2. A continuous 𝑛-linear form 𝑇 on a Banach space 𝐸 is called norm-peak if there is a unique (π‘₯1, … , π‘₯𝑛) ∈ 𝐸𝑛 such that β•‘π‘₯1β•‘ = … = β•‘π‘₯𝑛║ = 1 and for the multilinear operator norm it holds ‖𝑇 β€– = |𝑇 (π‘₯1, … , π‘₯𝑛)|.

Let 0 ≀ πœƒ ≀ Ο€2Β andΒ Β l∞,ΞΈ2= ℝ2 with the rotated supremum norm β€–(π‘₯, 𝑦)β€–(∞,πœƒ) = max {|π‘₯ cos πœƒ + 𝑦 sin πœƒ|, |π‘₯ sin πœƒ βˆ’ 𝑦 cos πœƒ|}.

In this note, we characterize all norm-peak multilinear forms on l∞,ΞΈ2. As a corollary we characterize all norm-peak multilinear forms on lp2 = ℝ2 with the 𝓁𝑝-norm for 𝑝 = 1, ∞.

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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 
  • Ε½eljka 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
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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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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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