# 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

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topCobos, 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

top- [1] A. Cayley, On a theory of determinants, Cambridge Philos. Soc. Trans. 8 (1843), 1-16.
- [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] 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] 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] J. A. Dieudonné and J. B. Carrell, Invariant Theory, Old and New, Academic Press, New York and London, 1971. Zbl0258.14011
- [6] I. M. Gel'fand, M. M. Kapranov and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Birkhäuser, Boston, MA, 1994. Zbl0827.14036
- [7] R. Grząślewicz and K. John, Extreme elements of the unit ball of bilinear operators on ${\ell}_{2}^{2}$, Arch. Math. (Basel) 50 (1988), 264-269. Zbl0653.47024
- [8] R. V. Kadison, Isometries of operator algebras, Ann. of Math. 54 (1951), 325-338. Zbl0045.06201
- [9] E. Schwartz, Über binäre trilineare Formen, Math. Z. 12 (1922), 18-35. Zbl48.0104.03

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