Paracommutators. Brief introduction, open problems.

Jaak Peetre

Revista Matemática de la Universidad Complutense de Madrid (1989)

  • Volume: 2, Issue: SUPL., page 201-211
  • ISSN: 1139-1138

Abstract

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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.

How to cite

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Peetre, Jaak. "Paracommutators. Brief introduction, open problems.." Revista Matemática de la Universidad Complutense de Madrid 2.SUPL. (1989): 201-211. <http://eudml.org/doc/43487>.

@article{Peetre1989,
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.},
author = {Peetre, Jaak},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Operadores integrales; multilinear forms in abstract Hilbert space; group representations; paracommutators over stratified groups; Heisenberg group; Schatten-von Neumann trace ideals},
language = {eng},
number = {SUPL.},
pages = {201-211},
title = {Paracommutators. Brief introduction, open problems.},
url = {http://eudml.org/doc/43487},
volume = {2},
year = {1989},
}

TY - JOUR
AU - Peetre, Jaak
TI - Paracommutators. Brief introduction, open problems.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1989
VL - 2
IS - SUPL.
SP - 201
EP - 211
AB - 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.
LA - eng
KW - Operadores integrales; multilinear forms in abstract Hilbert space; group representations; paracommutators over stratified groups; Heisenberg group; Schatten-von Neumann trace ideals
UR - http://eudml.org/doc/43487
ER -

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