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ON [Gfr ]p-CLASSES OF TRILINEAR FORMS

Published online by Cambridge University Press:  01 June 1999

FERNANDO COBOS ,
THOMAS KÜHN  and
JAAK PEETRE
FERNANDO COBOS
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, E-28040 Madrid, Spain, [email protected]
THOMAS KÜHN
Affiliation:
Fakultät für Mathematik und Informatik, Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany, [email protected]
JAAK PEETRE
Affiliation:
Matematiska institutionen, Lunds universitet, Box 118, S-221 00 Lund, Sweden, [email protected]
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Abstract

In a previous paper, the authors laid the foundations of a theory of Schatten–von Neumann classes [Gfr ]p (0<p[les ]∞) of trilinear forms in Hilbert space. This paper continues that research. In the n-dimensional case, it is shown that the best constant dˆ 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 two-bounded forms. Finally, the domination problem is investigated in the trilinear set-up.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 1003 - 1022
Copyright
The London Mathematical Society 1999

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