Extreme points of the complex binary trilinear ball
Cobos, Fernando ; Kühn, Thomas ; Peetre, Jaak
Studia Mathematica, Tome 141 (2000), p. 81-92 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space ℂ2. This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space ℝ2. As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216691 
@article{bwmeta1.element.bwnjournal-article-smv138i1p81bwm,
     author = {Fernando Cobos and Thomas K\"uhn and Jaak Peetre},
     title = {Extreme points of the complex binary trilinear ball},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {81-92},
     zbl = {0956.46013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv138i1p81bwm}
}

Cobos, Fernando; Kühn, Thomas; Peetre, Jaak. Extreme points of the complex binary trilinear ball. Studia Mathematica, Tome 141 (2000) pp. 81-92. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv138i1p81bwm/

[00000] [1] A. Cayley, On a theory of determinants, Cambridge Philos. Soc. Trans. 8 (1843), 1-16.

[00001] [2] F. Cobos, T. Kühn and J. Peetre, Schatten-von Neumann classes of multilinear forms, Duke Math. J. 65 (1992), 121-156. | Zbl 0779.47016

[00002] [3] F. Cobos, T. Kühn and J. Peetre, On Sp-classes of trilinear forms, J. London Math. Soc. (2) 59 (1999), 1003-1022. | Zbl 0935.47022

[00003] [4] F. Cobos, T. Kühn and J. Peetre, On the structure of bounded trilinear forms, http:/www.maths.lth.se/matematiklu/personal/jaak. | Zbl 1279.47013

[00004] [5] J. A. Dieudonné and J. B. Carrell, Invariant Theory, Old and New, Academic Press, New York and London, 1971. | Zbl 0258.14011

[00005] [6] I. M. Gel'fand, M. M. Kapranov and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Birkhäuser, Boston, MA, 1994. | Zbl 0827.14036

[00006] [7] R. Grząślewicz and K. John, Extreme elements of the unit ball of bilinear operators on ℓ22, Arch. Math. (Basel) 50 (1988), 264-269. | Zbl 0653.47024

[00007] [8] R. V. Kadison, Isometries of operator algebras, Ann. of Math. 54 (1951), 325-338. | Zbl 0045.06201

[00008] [9] E. Schwartz, Über binäre trilineare Formen, Math. Z. 12 (1922), 18-35. | Zbl 48.0104.03