Extreme points of the complex binary trilinear ball

Fernando Cobos; Thomas Kühn; Jaak Peetre

Studia Mathematica (2000)

  • Volume: 138, Issue: 1, page 81-92
  • ISSN: 0039-3223

Abstract

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We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space ℂ 2 . This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space ℝ 2 . As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.

How to cite

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Cobos, Fernando, Kühn, Thomas, and Peetre, Jaak. "Extreme points of the complex binary trilinear ball." Studia Mathematica 138.1 (2000): 81-92. <http://eudml.org/doc/216691>.

@article{Cobos2000,
abstract = {We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space $ℂ^2$. This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space $ℝ^2$. As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.},
author = {Cobos, Fernando, Kühn, Thomas, Peetre, Jaak},
journal = {Studia Mathematica},
keywords = {trilinear form; norm; Hilbert-Schmidt norm; extreme point; extreme point of unit ball},
language = {eng},
number = {1},
pages = {81-92},
title = {Extreme points of the complex binary trilinear ball},
url = {http://eudml.org/doc/216691},
volume = {138},
year = {2000},
}

TY - JOUR
AU - Cobos, Fernando
AU - Kühn, Thomas
AU - Peetre, Jaak
TI - Extreme points of the complex binary trilinear ball
JO - Studia Mathematica
PY - 2000
VL - 138
IS - 1
SP - 81
EP - 92
AB - We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space $ℂ^2$. This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space $ℝ^2$. As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.
LA - eng
KW - trilinear form; norm; Hilbert-Schmidt norm; extreme point; extreme point of unit ball
UR - http://eudml.org/doc/216691
ER -

References

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  1. [1] A. Cayley, On a theory of determinants, Cambridge Philos. Soc. Trans. 8 (1843), 1-16. 
  2. [2] F. Cobos, T. Kühn and J. Peetre, Schatten-von Neumann classes of multilinear forms, Duke Math. J. 65 (1992), 121-156. Zbl0779.47016
  3. [3] F. Cobos, T. Kühn and J. Peetre, On S p -classes of trilinear forms, J. London Math. Soc. (2) 59 (1999), 1003-1022. Zbl0935.47022
  4. [4] F. Cobos, T. Kühn and J. Peetre, On the structure of bounded trilinear forms, http:/www.maths.lth.se/matematiklu/personal/jaak. Zbl1279.47013
  5. [5] J. A. Dieudonné and J. B. Carrell, Invariant Theory, Old and New, Academic Press, New York and London, 1971. Zbl0258.14011
  6. [6] I. M. Gel'fand, M. M. Kapranov and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Birkhäuser, Boston, MA, 1994. Zbl0827.14036
  7. [7] R. Grząślewicz and K. John, Extreme elements of the unit ball of bilinear operators on ℓ 2 2 , Arch. Math. (Basel) 50 (1988), 264-269. Zbl0653.47024
  8. [8] R. V. Kadison, Isometries of operator algebras, Ann. of Math. 54 (1951), 325-338. Zbl0045.06201
  9. [9] E. Schwartz, Über binäre trilineare Formen, Math. Z. 12 (1922), 18-35. Zbl48.0104.03

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