Skip to main content
Log in

Lie isomorphisms of reflexive algebras. II

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

By characterizing minimal non-central Lie ideals, we describe the structure of Lie isomorphisms of reflexive algebras with J-subspace lattices. This result can apply to reflexive algebras with atomic Boolean subspace lattices or with pentagon subspace lattice algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. I. Beidar, M. Brešar, M. A. Chebotar and W. S. Martindale III, On Herstein’s Lie map conjectures. I, Transactions of the American Mathematical Society 353 (2001), 4235-p4260.

    Article  MathSciNet  MATH  Google Scholar 

  2. D. Benkovic and D. Eremita, Commuting traces and commutativity preserving maps on triangular algebras, Journal of Algebra 280 (2004), 797–824.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Brešar, Commuting maps: A survey, Taiwanese Journal of Mathematics 8 (2004), 361–397.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Katavolos, M. S. Lambrou and W. E. Longstaff, Pentagon subspace lattices on Banach spaces, Journal of Operator Theory 46 (2001), 355–380.

    MathSciNet  MATH  Google Scholar 

  5. W. E. Longstaff, Operators of rank one in reflexive algebras, Canadian Journal of Mathematics 28 (1976), 19–23.

    Article  MathSciNet  MATH  Google Scholar 

  6. W. E. Longstaff and Q. Panaia, J-subspace lattice and subspace M-bases, Studia Mathematica 139 (2000), 197–211.

    MathSciNet  MATH  Google Scholar 

  7. W. E. Longstaff, J. B. Nation and O. Panaia, Abstract reflexive sublattices and completely distributive collapsibility, Bulletin of the Australian Mathematical Society 58 (1998), 245–260.

    Article  MathSciNet  MATH  Google Scholar 

  8. F. Lu, Lie isomorphisms of reflexive algebras, Journal of Functional Analysis 240 (2006), 84–104.

    Article  MathSciNet  MATH  Google Scholar 

  9. F. Lu, Lie derivations of J-subspace lattice algebras, Proceedings of the American Mathematical Society 135 (2007), 2581–2590.

    Article  MathSciNet  MATH  Google Scholar 

  10. F. Lu and P. Li, Algebraic isomorphisms and Jordan derivations of J-subspace lattice algebras, Studia Mathematica 158 (2003), 287–301.

    Article  MathSciNet  MATH  Google Scholar 

  11. L. W. Marcoux and A. R. Sourour, Lie isomorphisms of nest algebras, Journal of Functional Analysis 164 (1999), 163–180.

    Article  MathSciNet  MATH  Google Scholar 

  12. C. R. Miers, Lie isomorphisms of factors, Transactions of the American Mathematical Society 147 (1970), 55–63.

    Article  MathSciNet  MATH  Google Scholar 

  13. X. Qi, J. Hou and J. Deng, Lie ring isomorphisms between nest algebras on Banach spaces, Journal of Functional Analysis 266 (2014), 4266–4292.

    Article  MathSciNet  MATH  Google Scholar 

  14. P. Šemrl, Linear maps that preserve the nilpotent operators, Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum 61 (1995), 523–534.

    MathSciNet  MATH  Google Scholar 

  15. T. Wang and F. Lu, Lie isomorphisms of nest algebras on Banach spaces, Journal of Mathematical Analysis and Applications 391 (2012), 582–594.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fangyan Lu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, C., Lu, F. Lie isomorphisms of reflexive algebras. II. Isr. J. Math. 227, 827–841 (2018). https://doi.org/10.1007/s11856-018-1743-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-018-1743-8

Navigation