caa a22 4500 386307660 CHVBK 20180307111534.0 cr unu---uuuuu 161130e198808 xx s 000 0 eng 10.1017/S1446788700032262 doi S1446788700032262 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700032262 Cowling Michael School of Mathematics University of New South Wales P. O. Box 1 Kensington. N.S.W. 2033, Australia On the characters of unitary representations [Elektronische Daten] [Michael Cowling] Let G be a locally compact group, and let D(G) be a dense subalgebra of the convolution algebra L1(G). Suppose that π is a unitary representation of G and that, for each u in D(G), π(u)) is a trace-class operator. Then the linear functional u → tr(π(u)) (the trace of π(u)) is called the D-character of π. We give a simple proof that the D-character of such a representation determines the representation up to unitary equivalence. As an application, we give an easy proof of the result of Harish-Chandra that the K-finite characters of unitary representations of semisimple Lie groups determine the representations. Copyright © Australian Mathematical Society 1988 22 D 10 nationallicence 22 D 25 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 45/1(1988-08), 62-65 1446-7887 45:1<62 1988 45 JAZ https://doi.org/10.1017/S1446788700032262 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700032262 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Cowling Michael School of Mathematics University of New South Wales P. O. Box 1 Kensington. N.S.W. 2033, Australia NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 45/1(1988-08), 62-65 1446-7887 45:1<62 1988 45 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge