caa a22 4500 388046872 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199806 xx s 000 0 eng 10.1017/S1446788700039161 doi S1446788700039161 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700039161 Extremally rich C*-crossed products and the cancellation property [Elektronische Daten] A unital C*-algebra A is called extremally rich if the set of quasi-invertible elements A-1 ex (A)A-1 (= A-1q) is dense in A, where ex(A) is the set of extreme points in the closed unit ball A1 of A. In [7, 8] Brown and Pedersen introduced this notion and showed that A is extremally rich if and only if conv(ex(A)) = A1. Any unital simple C*-algebra with extremal richness is either purely infinite or has stable rank one (sr(A) = 1). In this note we investigate the extremal richness of C*-crossed products of extremally rich C*-algebras by finite groups. It is shown that if A is purely infinite simple and unital then A xα, G is extremally rich for any finite group G. But this is not true in general when G is an infinite discrete group. If A is simple with sr(A) =, and has the SP-property, then it is shown that any crossed product A xα G by a finite abelian group G has cancellation. Moreover if this crossed product has real rank zero, it has stable rank one and hence is extremally rich. Copyright © Australian Mathematical Society 1998 46L05 nationallicence Jeong Ja A. Department of Mathematics Kyung Hee University Seoul, 130 - 701, Korea Osaka Hiroyuki Mathematics Institute University of Copenhagen Universitetsparken 5 DK-2100, Copenhagen Ø Denmark and Department of Mathematics Sciences Ryukyu University Nishihara-cho, Okinawn 903 - 01, Japan Journal of the Australian Mathematical Society Cambridge University Press 64/3(1998-06), 285-301 1446-7887 64:3<285 1998 64 JAZ https://doi.org/10.1017/S1446788700039161 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700039161 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jeong Ja A. Department of Mathematics Kyung Hee University Seoul, 130 - 701, Korea NATIONALLICENCE 700 1- Osaka Hiroyuki Mathematics Institute University of Copenhagen Universitetsparken 5 DK-2100, Copenhagen Ø Denmark and Department of Mathematics Sciences Ryukyu University Nishihara-cho, Okinawn 903 - 01, Japan NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 64/3(1998-06), 285-301 1446-7887 64:3<285 1998 64 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge