Extreme points of the complex binary trilinear ball

• Autorzy: Fernando Cobos , Thomas Kühn , Jaak Peetre
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 46B20: Geometry and structure of normed linear spaces
• 15A69: Multilinear algebra, tensor products

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 138
• Numer: 1
• Strony: 81-92

Daty

wydano

2000

otrzymano

1999-04-23

poprawiono

1999-11-03

Twórcy

autor

Fernando Cobos

• Departamento de Análisis Matemático, Facultad de Matemáticas Universidad, Complutense de Madrid, E-28040 Madrid, Spain

autor

Thomas Kühn

• Fakultät für Mathematik und Informatik, Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany

autor

Jaak Peetre

• Matematiska institutionen, Lunds universitet, Box 118, S-22100 Lund, Sweden

Bibliografia

• [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.
• [3] F. Cobos, T. Kühn and J. Peetre, On $S_p$-classes of trilinear forms, J. London Math. Soc. (2) 59 (1999), 1003-1022.
• [4] F. Cobos, T. Kühn and J. Peetre, On the structure of bounded trilinear forms, http:/www.maths.lth.se/matematiklu/personal/jaak.
• [5] J. A. Dieudonné and J. B. Carrell, Invariant Theory, Old and New, Academic Press, New York and London, 1971.
• [6] I. M. Gel'fand, M. M. Kapranov and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Birkhäuser, Boston, MA, 1994.
• [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.
• [8] R. V. Kadison, Isometries of operator algebras, Ann. of Math. 54 (1951), 325-338.
• [9] E. Schwartz, Über binäre trilineare Formen, Math. Z. 12 (1922), 18-35.