Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 11
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Huang, Li and Liu, Yanxiao 2014. Maps completely preserving commutativity and maps completely preserving Jordan zero-product. Linear Algebra and its Applications, Vol. 462, p. 233.


    Yao, Hongmei Zheng, Baodong and Hong, Gang 2012. Maps Completely Preserving Involutions and Maps Completely Preserving Drazin Inverse. ISRN Applied Mathematics, Vol. 2012, p. 1.


    Chuang, Chen-Lian and Lee, Tsiu-Kwen 2011. Derivations modulo elementary operators. Journal of Algebra, Vol. 338, Issue. 1, p. 56.


    Cui, Jian Lian 2011. Nonlinear preserver problems on B(H). Acta Mathematica Sinica, English Series, Vol. 27, Issue. 1, p. 193.


    Huang, Li and Hou, Jinchuan 2011. Maps completely preserving spectral functions. Linear Algebra and its Applications, Vol. 435, Issue. 11, p. 2756.


    Hou, Jinchuan and Huang, Li 2010. Maps completely preserving idempotents and maps completely preserving square-zero operators. Israel Journal of Mathematics, Vol. 176, Issue. 1, p. 363.


    Zhu, Jun Xiong, Changping and Zhu, Hong 2010. Multiplicative mappings at some points on matrix algebras. Linear Algebra and its Applications, Vol. 433, Issue. 5, p. 914.


    Hou, Jinchuan and Huang, Li 2009. Characterizing isomorphisms in terms of completely preserving invertibility or spectrum. Journal of Mathematical Analysis and Applications, Vol. 359, Issue. 1, p. 81.


    Zhang, Jian-Hua Yang, An-Li and Pan, Fang-Fang 2006. Linear maps preserving zero products on nest subalgebras of von Neumann algebras. Linear Algebra and its Applications, Vol. 412, Issue. 2-3, p. 348.


    Hadwin, Don and Li, Jiankui 2004. Local derivations and local automorphisms. Journal of Mathematical Analysis and Applications, Vol. 290, Issue. 2, p. 702.


    Hou, Jinchuan and Zhang, Xiuling 2004. Ring isomorphisms and linear or additive maps preserving zero products on nest algebras. Linear Algebra and its Applications, Vol. 387, p. 343.


    ×
  • Bulletin of the Australian Mathematical Society, Volume 65, Issue 1
  • February 2002, pp. 79-91

Linear maps on von Neumann algebras preserving zero products on tr-rank

  • Cui Jianlian (a1) (a2) and Hou Jinchuan (a3) (a4)
  • DOI: http://dx.doi.org/10.1017/S0004972700020086
  • Published online: 01 April 2009
Abstract

In this paper, we give some characterisations of homomorphisms on von Neumann algebras by linear preservers. We prove that a bounded linear surjective map from a von Neumann algebra onto another is zero-product preserving if and only if it is a homomorphism multiplied by an invertible element in the centre of the image algebra. By introducing the notion of tr-rank of the elements in finite von Neumann algebras, we show that a unital linear map from a linear subspace ℳ of a finite von Neumann algebra ℛ into ℛ can be extended to an algebraic homomorphism from the subalgebra generated by ℳ into ℛ; and a unital self-adjoint linear map from a finite von Neumann algebra onto itself is completely tr-rank preserving if and only if it is a spatial *-automorphism.

    • 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.

      Linear maps on von Neumann algebras preserving zero products on tr-rank
      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.

      Linear maps on von Neumann algebras preserving zero products on tr-rank
      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.

      Linear maps on von Neumann algebras preserving zero products on tr-rank
      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]L.G. Brown and G.K. Pedersen , ‘C*-algebras of real rank zero’, J. Funct. Anal. 99 (1991), 131149.

[3]W. Chooi and M. Lim , ‘Linear preserves on triangular matrices’, Linear Algebra Appl. 269 (1998), 241255.

[4]J. Cui , J. Hou and B. Li , ‘Linear preservers on upper triangular operator matrix algebras’, Linear Algebra Appl. 336 (2001), 2950.

[8]J. Hou , ‘Multiplicative maps on ℬ(X)’, Sci. China Ser. A 41 (1998), 337345.

[12]M. Lim , ‘Rank and tensor rank preservers’, Linear and Multilinear Algebra 33 (1992), 721.

[13]L. Molnar , ‘Some linear preserver problems on ℬ(H) concerning rank and corank’, Linear Algebra Appl. 286 (1999), 311321.

[14]L. Molnar and P. Semrl , ‘Some linear preserver problems on upper triangular matrices’, Linear and Multilinear Algebra 45 (1998), 189206.

Recommend this journal

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

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax