Note on Trace Class Groups
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Publication:6317800
arXiv1904.11789MaRDI QIDQ6317800
Publication date: 26 April 2019
Abstract: A Lie group G is called a trace class group if for every irreducible unitary representation R of G and every C-infinity function f with compact support the operator R(f) is of trace class. In this note we prove that the semidirect product of R^n and a real semisimple algebraic subgroup G of GL(n;R) is a trace class group only if G is compact. The converse has been shown elsewhere. We also make a descent start with the study of semidirect products with Heisenberg-type groups.
Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Unitary representations of locally compact groups (22D10) Analysis on other specific Lie groups (43A80)
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