Geodesic
Automatic continuity of biorthogonality preservers between weakly compact $JB^*$-triples and atomic $JBW^*$-triples
María Burgos 1   ; Jorge J. Garcés 1   ; Antonio M. Peralta 1
1 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain
Studia Mathematica, Tome 204 (2011) no. 2, pp. 97-121 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove that every biorthogonality preserving linear surjection from a weakly compact $JB^*$-triple containing no infinite-dimensional rank-one summands onto another $JB^*$-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic $JBW^*$-triples containing no infinite-dimensional rank-one summands is automatically continuous. Consequently, two atomic $JBW^*$-triples containing no rank-one summands are isomorphic if and only if there exists a (not necessarily continuous) biorthogonality preserving linear surjection between them.
DOI : 10.4064/sm204-2-1
Keywords: prove every biorthogonality preserving linear surjection weakly compact * triple containing infinite dimensional rank one summands another * triple automatically continuous every biorthogonality preserving linear surjection between atomic jbw * triples containing infinite dimensional rank one summands automatically continuous consequently atomic jbw * triples containing rank one summands isomorphic only there exists necessarily continuous biorthogonality preserving linear surjection between

María Burgos  1   ; Jorge J. Garcés  1   ; Antonio M. Peralta  1

1 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain 
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María Burgos; Jorge J. Garcés; Antonio M. Peralta. Automatic continuity of biorthogonality preservers between weakly compact $JB^*$-triples and atomic $JBW^*$-triples. Studia Mathematica, Tome 204 (2011) no. 2, pp. 97-121. doi: 10.4064/sm204-2-1

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