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On G p ‐Classes of Trilinear Forms
Author(s) -
Cobos Fernando,
Kühn Thomas,
Peetre Jaak
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007504
Subject(s) - mathematics , bounded function , norm (philosophy) , hilbert space , banach space , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , law , political science
In a previous paper, the authors laid the foundations of a theory of Schatten–von Neumann classes G 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 d̂ 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.