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The Quarterly Journal of Mathematics Advance Access originally published online on February 7, 2006
The Quarterly Journal of Mathematics 2006 57(4):505-525; doi:10.1093/qmath/hal001
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© The author 2006. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

ON THE MANIFOLD OF COMPLEMENTED PRINCIPAL INNER IDEALS IN JB*-TRIPLES

José M. Isidro1,{dagger} and László L. Stachó2

1 Facultad de Matemáticas, Santiago de Compostela, Spain
2 Bolyai Institute, 6720 Szeged, Hungary

{dagger} Corresponding author. E-mail: jmisidro{at}zmat.usc.es


  Abstract

The set M of Neher's classes of tripotents in an arbitrary JB*-triple Z is considered and a natural complex-analytic Banach manifold structure is defined on it. The relationship between M and the Grassmann manifold of all complemented principal inner ideals in Z is studied in detail, and the smooth complete vector fields on M are characterized as smooth complete equivariant vector fields on the manifold M of tripotents of Z.


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