Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 10
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Pasnicu, Cornel and Phillips, N. Christopher 2015. Crossed products by spectrally free actions. Journal of Functional Analysis, Vol. 269, Issue. 4, p. 915.


    Phillips, N. Christopher Sørensen, Adam P.W. and Thiel, Hannes 2015. Semiprojectivity with and without a group action. Journal of Functional Analysis, Vol. 268, Issue. 4, p. 929.


    RØRDAM, MIKAEL and SIERAKOWSKI, ADAM 2012. Purely infinite C*-algebras arising from crossed products. Ergodic Theory and Dynamical Systems, Vol. 32, Issue. 01, p. 273.


    Yang, Xinbing and Fang, Xiaochun 2012. The Tracial Class Property for Crossed Products by Finite Group Actions. Abstract and Applied Analysis, Vol. 2012, p. 1.


    Hua, Jiajie 2010. The tracial Rokhlin property for automorphisms on non-simple C*-algebras. Chinese Annals of Mathematics, Series B, Vol. 31, Issue. 2, p. 191.


    Fan, Qingzhai and Fang, Xiaochun 2009. Stable rank one and real rank zero for crossed products by finite group actions with the tracial Rokhlin property. Chinese Annals of Mathematics, Series B, Vol. 30, Issue. 2, p. 179.


    Koliha, J.J. Djordjević, Dragan and Cvetković, Dragana 2007. Moore–Penrose inverse in rings with involution. Linear Algebra and its Applications, Vol. 426, Issue. 2-3, p. 371.


    OSAKA, HIROYUKI and TERUYA, TAMOTSU 2006. TOPOLOGICAL STABLE RANK OF INCLUSIONS OF UNITAL C*-ALGEBRAS. International Journal of Mathematics, Vol. 17, Issue. 01, p. 19.


    Lin, Huaxin and Osaka, Hiroyuki 2005. The Rokhlin property and the tracial topological rank. Journal of Functional Analysis, Vol. 218, Issue. 2, p. 475.


    OSAKA, Hiroyuki 2003. Non-Commutative Dimension for C*-Algebras. Interdisciplinary Information Sciences, Vol. 9, Issue. 2, p. 209.


    ×
  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 64, Issue 3
  • June 1998, pp. 285-301

Extremally rich C*-crossed products and the cancellation property

  • Ja A Jeong (a1) and Hiroyuki Osaka (a2)
  • DOI: http://dx.doi.org/10.1017/S1446788700039161
  • Published online: 01 April 2009
Abstract
Abstract

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 xαG 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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Extremally rich C*-crossed products and the cancellation property
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Extremally rich C*-crossed products and the cancellation property
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Extremally rich C*-crossed products and the cancellation property
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[2]B. Blackadar , K-theory for operator algebras (Springer, New York, 1986).

[4]B. Blackadar , ‘Symmetries on the CAR algebra’, Ann. of Math. 131 (1990), 589623.

[5]B. Blackadar and A. Kumjian , ‘Skew products of relations and the structure of simple C*-algebras’, Math. Z. 189 (1985), 5563.

[6]L. G. Brown and G. K. Pedersen , ‘C*-algebras of real rank zero’, J. Funct. Anal. 99 (1991), 131149.

[11]J. Cuntz , ‘K-theory for certain C*-algebras’, Annals of Math. 113 (1981), 181197.

[12]G. A. Elliott , ‘A classification of certain simple C*-algebras’, in: Quantum and non-commutative analysis (eds. H. Araki ) (Kluwer Academic Publisher, Dordrecht, 1993) pp. 373385.

[13]J. A. Jeong , ‘Purely infinite simple crossed products’, Proc. Amer. Math. Soc. 123 (1995), 30753078.

[14]J. A. Jeong , K. Kodaka and H. Osaka , ‘Purely infinite simple C*-crossed products II’, Canad. Math. Bull. 39 (1996), 203210.

[15]A. Kishimoto , ‘Outer automorphisms and related crossed products of simple C*-algebras’, Comm. Math. Phys. 81 (1981), 429435.

[18]H. Lin , ‘Generalized Weyl-von Neumann theorems’, Internat. J. Math. 2 (1991), 725739.

[21]D. Olsen , G. K. Pedersen and E. Størmer , ‘Compact abelian groups of automorphisms of simple C*-algebras’, Invent. Math. 39 (1977), 5564.

[26]M. Rørdam , ‘On the structure of simple C*-algebras tensored with a UHF-algebra’, J. Funct. Anal. 100 (1991), 117.

[27]J. Rosenberg , ‘Appendix to O. Bratteli's paper on crossed products of UHF-algebras’, Duke Math. J. 46 (1979), 2526.

[29]S. Zhang , ‘A property of purely infinite simple C*-algebras’, Proc. Amer. Math. Soc. 109 (1990), 717720.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: