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$% J. Peetre, Paracommutators Brief introduction, open problems, Rev. Mat. Univ. Complut. Madrid 2 (1989), supplementary, 201–211.%$

Paracommutators Brief Introduction, Open Problems

Jaak PEETRE
Matematiska institutionen
Box 6701
S-11385 Stockholm Sweden
Departamento de Matemáticas
Universidad Autónoma de Madrid
28049 Madrid Spain

ABSTRACT

We review the basic facts about the theory of paracommutators in Rn (sec S. Janson, J. Peetre, Trans. Am. Math. Soc. 305 (1988), 467504). We also give an interpretation of paracommutators from the point of view of group representations. This suggests a generalization to more general groups. Here we sketch a theory of paracommutators over stratified groups. This include the famous Heisenberg group. Finally, we take up the question of generalizing the notion of Schatten-von Neumann trace ideals to the case of multilinear forms in (abstract) Hilbert spaces.

1980 Mathematics Subject Classification (1985 revision): 47B35, 46E35, 36M35, 47D25.