Complutense University Library

On G(p)-classes of trilinear forms

Cobos, Fernando and Kuehn, Thomas and Peetre, Jaak (1999) On G(p)-classes of trilinear forms. Journal of the London Mathematical Society. Second Series, 59 (3). pp. 1003-1022. ISSN 0024-6107

[img] PDF
Restricted to Repository staff only

321kB

Official URL: http://jlms.oxfordjournals.org/content/59/3/1003.full.pdf+html

View download statistics for this eprint

==>>> Export to other formats

Abstract

In a previous paper, the authors laid the foundations of a theory of Schatten±von Neumann classes 'p
(0!p%¢) of trilinear forms in Hilbert space. This paper continues that research. In the n-dimensional
case, it is shown that the best constant d# that relates the Hilbert±Schmidt norm of a form with its bounded
norm behaves like n. Some results are also obtained in the quasi-Banach case (0!p!1), and for twobounded
forms. Finally, the domination problem is investigated in the trilinear set-up.


Item Type:Article
Uncontrolled Keywords:Two-boundedness; domination; Schatten-von Neumann classes; trilinear forms; quasi-Banach case
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15252
References:

J. Bergh and J. Lo$ fstro$m, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften 223 (Springer, 1976).

R. P. Boas, `Majorant problems for trigonometric series ', J. Anal. Math. 10 (1962}63) 253±271.

F. Cobos and T. Ku$ hn, `On a conjecture of Barry Simon on trace ideals ', Duke Math. J. 59 (1989)295±299.

F. Cobos, T. Ku$ hn and J. Peetre, `Schatten±von Neumann classes of multilinear forms', Duke Math. J. 65 (1992) 121±156.

M. De!champs-Gondin, F. Lust-Picard and H. Queffelec, `On the minorant properties in Cp(H) ', Paci®c J. Math. 119 (1985) 89±101.

M. Ledoux and M. Talagrand, Probability in Banach spaces, Ergebnisse der Mathematik und õ$hrer Grenzgebiete 23 (Springer, 1991).

J. Peetre, `Paracommutators and minimal spaces', Operators and function theory (ed. S. C. Power; Reidel, Dordrecht, 1985) 163±224.

J. Peetre, `Paracommutators ± a brief introduction, open problems', Re.. Mat. Uni.. Complut. Madrid 2 (1989) 201±211 (nu!mero suplementario).

V. V. Peller, `Hankel operators of class 'p and their applications (rational approximation, gaussian processes, the problem of majorizing operators)', Math. USSR Sbornik 41 (1982) 443±479.

A. Pietsch and H. Triebel, `Interpolationstheorie fu$ r Banachideale von beschra$nkten linearen Operatoren', Studia Math. 31 (1968) 95±109.

B. Simon, Trace ideals and their applications (Cambridge University Press, Cambridge, 1979).

B. Simon, `Pointwise domination of matrices and comparison of Cp norms', Paci®c J. Math. 97 (1981)471±475.

H. Triebel, `Zur Interpolationstheorie von Normidealen in Hilbertra$umen', Wiss. Z. Uni.. Jena 18 (1969) 263±267.

H. Triebel, Interpolation theory. Function spaces. Differential operators (VEB Deutscher Verlag der Wissenschaften, Berlin, 1978).

Deposited On:18 May 2012 10:12
Last Modified:06 Feb 2014 10:19

Repository Staff Only: item control page