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Von neumann regularity and quadratic conorms in JB*-triples and C*-algebras

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Abstract

We revise the notion of von Neumann regularity in JB*-triples by finding a new characterisation in terms of the range of the quadratic operator Q(a). We introduce the quadratic conorm of an element a in a JB*-triple as the minimum reduced modulus of the mapping Q(a). It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW*-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C*-algebras and von Neumann algebras are also studied.

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Authors and Affiliations

  1. Department of Algebra and Mathematical Analysis, University of Almería, 04120, Almería, Spain

    María Burgos, Amin El Kaidi & Antonio Morales Campoy

  2. Department of Mathematical Analysis, University of Granada, 18071, Granada, Spain

    Antonio M. Peralta

  3. Department of Algebra and Mathematical Analysis, University of Almería, 04120, Almería, Spain

    Maribel Ramírez

Authors
  1. María Burgos
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  2. Amin El Kaidi
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  3. Antonio Morales Campoy
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  4. Antonio M. Peralta
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  5. Maribel Ramírez
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Corresponding author

Correspondence to María Burgos.

Additional information

Authors partially supported by I+D MEC Projects No. MTM 2005-02541, MTM 2004-03882, Junta de Andalucía Grants FQM 0199,FQM 0194, FQM 1215 and the PCI Project No. A/4044/05 of the Spanish AECI

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Burgos, M., El Kaidi, A., Campoy, A.M. et al. Von neumann regularity and quadratic conorms in JB*-triples and C*-algebras. Acta. Math. Sin.-English Ser. 24, 185–200 (2008). https://doi.org/10.1007/s10114-007-0985-x

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  • DOI: https://doi.org/10.1007/s10114-007-0985-x

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